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The dataset generation failed
Error code: DatasetGenerationError
Exception: TypeError
Message: Couldn't cast array of type
struct<0: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 1: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 2: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 3: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 4: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 5: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 6: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 7: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 8: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 9: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 10: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 11: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 12: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 13: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>>
to
{'0': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '1': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '2': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '3': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '4': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '5': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '6': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '7': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '8': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '9': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '10': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}}
Traceback: Traceback (most recent call last):
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/builder.py", line 1831, in _prepare_split_single
writer.write_table(table)
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/arrow_writer.py", line 714, in write_table
pa_table = table_cast(pa_table, self._schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2272, in table_cast
return cast_table_to_schema(table, schema)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2224, in cast_table_to_schema
cast_array_to_feature(
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 1795, in wrapper
return pa.chunked_array([func(chunk, *args, **kwargs) for chunk in array.chunks])
^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/table.py", line 2092, in cast_array_to_feature
raise TypeError(f"Couldn't cast array of type\n{_short_str(array.type)}\nto\n{_short_str(feature)}")
TypeError: Couldn't cast array of type
struct<0: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 1: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 2: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 3: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 4: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 5: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 6: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 7: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 8: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 9: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 10: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 11: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 12: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>, 13: struct<type: string, sentence-1-token-indices: list<item: int64>, sentence-2-token-indices: list<item: int64>, intention: string>>
to
{'0': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '1': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '2': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '3': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '4': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '5': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '6': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '7': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '8': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '9': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}, '10': {'type': Value('string'), 'sentence-1-token-indices': List(Value('int64')), 'sentence-2-token-indices': List(Value('int64')), 'intention': Value('string')}}
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 1450, in compute_config_parquet_and_info_response
parquet_operations, partial, estimated_dataset_info = stream_convert_to_parquet(
^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/src/worker/job_runners/config/parquet_and_info.py", line 993, in stream_convert_to_parquet
builder._prepare_split(
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/builder.py", line 1702, in _prepare_split
for job_id, done, content in self._prepare_split_single(
^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/src/services/worker/.venv/lib/python3.12/site-packages/datasets/builder.py", line 1858, in _prepare_split_single
raise DatasetGenerationError("An error occurred while generating the dataset") from e
datasets.exceptions.DatasetGenerationError: An error occurred while generating the datasetNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
sentence-pair-index
int64 | page-sentence-1
int64 | type-sentence-1
string | id-sentence-1
string | num_section-sentence-1
int64 | page-sentence-2
int64 | type-sentence-2
string | id-sentence-2
string | num_section-sentence-2
int64 | text-sentence-1
string | text-sentence-2
string | edits-combination
dict | id_version_1
string | id_version_2
string | sentence_pair_id
string | num_paragraph-sentence-1
int64 | num_sentence-sentence-1
int64 | num_paragraph-sentence-2
int64 | num_sentence-sentence-2
int64 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0
| 0
|
Title
|
Y6LzLWXlS8E_00_00_00
| 0
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|
Title
|
WNev_iSes_00_00_00
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|
Deconfounded Imitation Learning
|
Deconfounded Imitation Learning
|
{
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WNev_iSes
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1
| 0
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Paragraph
|
Y6LzLWXlS8E_01_00_00
| 1
| null | null | null | null |
Anonymous Author(s)
|
{
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Y6LzLWXlS8E
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WNev_iSes
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|
2
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AffiliationAddress email
|
{
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}
|
Y6LzLWXlS8E
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WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00002
| 1
| 0
| null | null |
|
3
| 0
|
Abstract
|
Y6LzLWXlS8E_01_02_00
| 1
| 0
|
Abstract
|
WNev_iSes_01_00_00
| 1
|
Abstract
|
Abstract
|
{
"0": null,
"1": null,
"2": null,
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"5": null,
"6": null,
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00003
| 2
| 0
| 0
| 0
|
4
| 0
|
Abstract
|
Y6LzLWXlS8E_01_03_00
| 1
| 0
|
Abstract
|
WNev_iSes_01_01_00
| 1
|
Standard imitation learning can fail when the expert demonstrators have differentsensory inputs than the imitating agent.
|
Standard imitation learning can fail when the expert demonstrators have different sensory inputs than the imitating agent.
|
{
"0": {
"type": "Substitute",
"sentence-1-token-indices": [
72,
88
],
"sentence-2-token-indices": [
72,
89
],
"intention": "Improve-grammar-Typo"
},
"1": null,
"2": null,
"3": null,
"4": null,
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"6": null,
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"8": null,
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00004
| 3
| 0
| 1
| 0
|
5
| 0
|
Abstract
|
Y6LzLWXlS8E_01_03_01
| 1
| 0
|
Abstract
|
WNev_iSes_01_01_01
| 1
|
This partial observability gives rise tohidden confounders in the causal graph, which lead to the failure to imitate.
|
This is because partial observability gives rise to hidden confounders in the causal graph.
|
{
"0": {
"type": "Insertion",
"sentence-1-token-indices": null,
"sentence-2-token-indices": [
5,
15
],
"intention": "Content"
},
"1": {
"type": "Substitute",
"sentence-1-token-indices": [
39,
47
],
"sentence-2-token-indices": [
49,
58
],
"intention": "Improve-grammar-Typo"
},
"2": {
"type": "Substitute",
"sentence-1-token-indices": [
74,
118
],
"sentence-2-token-indices": [
85,
91
],
"intention": "Content"
},
"3": null,
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00005
| 3
| 1
| 1
| 1
|
6
| 0
|
Abstract
|
Y6LzLWXlS8E_01_03_02
| 1
| 0
|
Abstract
|
WNev_iSes_01_01_02
| 1
|
Webreak down the space of confounded imitation learning problems and identify threesettings with different data requirements in which the correct imitation policy canbe identified.
|
We break down the space of confounded imitation learning problems and identify three settings with different data requirements in which the correct imitation policy can be identified.
|
{
"0": {
"type": "Substitute",
"sentence-1-token-indices": [
0,
7
],
"sentence-2-token-indices": [
0,
8
],
"intention": "Improve-grammar-Typo"
},
"1": {
"type": "Substitute",
"sentence-1-token-indices": [
78,
91
],
"sentence-2-token-indices": [
79,
93
],
"intention": "Improve-grammar-Typo"
},
"2": {
"type": "Substitute",
"sentence-1-token-indices": [
163,
168
],
"sentence-2-token-indices": [
165,
171
],
"intention": "Improve-grammar-Typo"
},
"3": null,
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00006
| 3
| 2
| 1
| 2
|
7
| 0
|
Abstract
|
Y6LzLWXlS8E_01_03_03
| 1
| 0
|
Abstract
|
WNev_iSes_01_01_03
| 1
|
We then introduce an algorithm for deconfounded imitation learning,which trains an inference model jointly with a latent-conditional policy.
|
We then introduce an algorithm for deconfounded imitation learning, which trains an inference model jointly with a latent-conditional policy.
|
{
"0": {
"type": "Substitute",
"sentence-1-token-indices": [
58,
72
],
"sentence-2-token-indices": [
58,
73
],
"intention": "Improve-grammar-Typo"
},
"1": null,
"2": null,
"3": null,
"4": null,
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"6": null,
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"8": null,
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00007
| 3
| 3
| 1
| 3
|
8
| 0
|
Abstract
|
Y6LzLWXlS8E_01_03_04
| 1
| 0
|
Abstract
|
WNev_iSes_01_01_04
| 1
|
At testtime, the agent alternates between updating its belief over the latent and actingunder the belief.
|
At test time, the agent alternates between updating its belief over the latent and acting under the belief.
|
{
"0": {
"type": "Substitute",
"sentence-1-token-indices": [
3,
12
],
"sentence-2-token-indices": [
3,
13
],
"intention": "Improve-grammar-Typo"
},
"1": {
"type": "Substitute",
"sentence-1-token-indices": [
82,
93
],
"sentence-2-token-indices": [
83,
95
],
"intention": "Improve-grammar-Typo"
},
"2": null,
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"6": null,
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"8": null,
"9": null,
"10": null
}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00008
| 3
| 4
| 1
| 4
|
9
| 0
|
Abstract
|
Y6LzLWXlS8E_01_03_05
| 1
| 0
|
Abstract
|
WNev_iSes_01_01_05
| 1
|
We show in theory and practice that this algorithm convergesto the correct interventional policy, solves the confounding issue, and can undercertain assumptions achieve an asymptotically optimal imitation performance
|
We show in theory and practice that this algorithm converges to the correct interventional policy, solves the confounding issue, and can under certain assumptions achieve an asymptotically optimal imitation performance.
|
{
"0": {
"type": "Substitute",
"sentence-1-token-indices": [
51,
62
],
"sentence-2-token-indices": [
51,
63
],
"intention": "Improve-grammar-Typo"
},
"1": {
"type": "Substitute",
"sentence-1-token-indices": [
136,
148
],
"sentence-2-token-indices": [
137,
150
],
"intention": "Improve-grammar-Typo"
},
"2": {
"type": "Substitute",
"sentence-1-token-indices": [
205,
216
],
"sentence-2-token-indices": [
207,
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],
"intention": "Improve-grammar-Typo"
},
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00009
| 3
| 5
| 1
| 5
|
10
| 0
|
Section
|
Y6LzLWXlS8E_02_00_00
| 2
| 0
|
Section
|
WNev_iSes_02_00_00
| 2
|
Introduction
|
Introduction
|
{
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00010
| null | null | null | null |
11
| 0
|
Paragraph
|
Y6LzLWXlS8E_02_00_00
| 2
| 0
|
Paragraph
|
WNev_iSes_02_00_00
| 2
|
In imitation learning (IL), an agent learns a policy directly from expert demonstrations withoutrequiring the specification of a reward function.
|
In imitation learning (IL), an agent learns a policy directly from expert demonstrations without requiring the specification of a reward function.
|
{
"0": {
"type": "Substitute",
"sentence-1-token-indices": [
89,
105
],
"sentence-2-token-indices": [
89,
106
],
"intention": "Improve-grammar-Typo"
},
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00011
| 0
| 0
| 0
| 0
|
12
| 0
|
Paragraph
|
Y6LzLWXlS8E_02_00_01
| 2
| 0
|
Paragraph
|
WNev_iSes_02_00_01
| 2
|
This paradigm could be essential for solving realworld problems in autonomous driving and robotics where reward functions can be difficult to shapeand online learning may be dangerous.
|
This paradigm could be essential for solving realworld problems in autonomous driving and robotics where reward functions can be difficult to shape and online learning may be dangerous.
|
{
"0": {
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"sentence-1-token-indices": [
142,
150
],
"sentence-2-token-indices": [
142,
151
],
"intention": "Improve-grammar-Typo"
},
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00012
| 0
| 1
| 0
| 1
|
13
| 0
|
Paragraph
|
Y6LzLWXlS8E_02_00_02
| 2
| 0
|
Paragraph
|
WNev_iSes_02_00_02
| 2
|
However, standard IL requires that the conditions under whichthe agent operates exactly match those encountered by the expert.
|
However, standard IL requires that the conditions under which the agent operates exactly match those encountered by the expert.
|
{
"0": {
"type": "Substitute",
"sentence-1-token-indices": [
56,
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],
"sentence-2-token-indices": [
56,
65
],
"intention": "Improve-grammar-Typo"
},
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In particular, they assume thatthere are no latent confounders —variables that affect the expert behavior, but that are not observed bythe agent.
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In particular, they assume that there are no latent confounders —variables that affect the expert behavior, but that are not observed by the agent.
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This assumption is often unrealistic.
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This assumption is often unrealistic.
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Consider a human driver who is aware of the weatherforecast and lowers its speed in icy conditions, even if those are not visible from observations.
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Consider a human driver who is aware of the weather forecast and lowers its speed in icy conditions, even if those are not visible from observations.
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Animitator agent without access to the weather forecast will not be able to adapt to such conditions.
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An imitator agent without access to the weather forecast will not be able to adapt to such conditions.
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In such a situation, an imitating agent may take their own past actions as evidence for the values ofthe confounder.
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In such a situation, an imitating agent may take their own past actions as evidence for the values of the confounder.
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A self-driving car, for instance, could conclude that it is driving fast, thus there can beno ice on the road.
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A self-driving car, for instance, could conclude that it is driving fast, thus there can be no ice on the road.
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This issue of causal delusion was first pointed out in Ortega and Braun [2010a,b]and studied in more depth by Ortega et al.
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This issue of causal delusion was first pointed out in Ortega and Braun [2010a,b] and studied in more depth by Ortega et al.
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The authors analyze the causal structure of thisproblem and argue that an imitator needs to learn a policy that corresponds to a certain interventionaldistribution.
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The authors analyze the causal structure of this problem and argue that an imitator needs to learn a policy that corresponds to a certain interventional distribution.
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They then show that the classic DAgger algorithm [Ross et al., 2011], which requiresquerying experts at each time step, solves this problem and converges to the interventional policy.
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They then show that the classic DAgger algorithm [Ross et al., 2011], which requires querying experts at each time step, solves this problem and converges to the interventional policy.
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In this paper, we present a solution to a confounded IL problem, where both the expert policy andthe environment dynamics are Markovian.
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In this paper, we present a solution to a confounded IL problem, where both the expert policy and the environment dynamics are Markovian.
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The solution does not require querying experts.
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The solution does not require querying experts.
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We firstpresent a characterization of confounded IL problems depending on properties of the environmentand expert policy (section 3).
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We first present a characterization of confounded IL problems depending on properties of the environment and expert policy (Section 3).
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We then show theoretically that an imitating agent can learn behaviorsthat approach optimality when the above Markov assumptions and a recurrence property hold.
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We then show theoretically that an imitating agent can learn behaviors that approach optimality when the above Markov assumptions and a recurrence property hold.
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We then introduce a practical algorithm for deconfounded imitation learning that does not require expert queries (section 4).
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We then introduce a practical algorithm for deconfounded imitation learning that does not require expert queries (Section 4).
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An agent jointly learns an inference network for the valueof latent variables that explain the environment dynamics as well as a latent-conditional policy.
|
An agent jointly learns an inference network for the value of latent variables that explain the environment dynamics as well as a latent-conditional policy.
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At test time, the agent iteratively samples latents from its belief, acts in the environ- ment, and updates the belief based on the environment dynamics.
|
At test time, the agent iteratively samples latents from its belief, acts in the environment, and updates the belief based on the environment dynamics.
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An imitator steering a selfdriving car, for instance, would learn how to infer the weather condition from the dynamics ofthe car on the road.
|
An imitator steering a self-driving car, for instance, would learn how to infer the weather condition from the dynamics of the car on the road.
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WNev_iSes_02_03_04
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This inference model can be applied both to its own online experienceas well as to expert trajectories, allowing it to imitate the behavior adequate for the weather.
|
This inference model can be applied both to its own online experience as well as to expert trajectories, allowing it to imitate the behavior adequate for the weather.
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Y6LzLWXlS8E.WNev_iSes.00031
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Y6LzLWXlS8E_02_05_00
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Figure
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WNev_iSes_02_04_00
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[Figure]
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[Figure]
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Finally, our deconfounded imitation learning algorithm isdemonstrated in a multi-armed bandit problem.
|
Finally, our deconfounded imitation learning algorithm is demonstrated in a multi-armed bandit problem.
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We showthat the agent quickly adapts to the unobserved propertiesof the environment and then behaves optimally (section 5).
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We show that the agent quickly adapts to the unobserved properties of the environment and then behaves optimally (Section 5).
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Section
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Y6LzLWXlS8E_03_00_00
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Section
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WNev_iSes_03_00_00
| 3
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Imitation learning and latent confounders
|
Imitation learning and latent confounders
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WNev_iSes_03_00_00
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We begin by introducing the problem of confounded imitation learning.
|
We begin by introducing the problem of confounded imitation learning.
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Following Ortega et al.
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Following Ortega et al.
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WNev_iSes_03_00_02
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[2021], we discusshow behavioral cloning fails in the presence of latent confounders.
|
[2021], we discuss how behavioral cloning fails in the presence of latent confounders.
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We then define the interventional policy, whichsolves the problem of confounded imitation learning.
|
We then define the interventional policy, which solves the problem of confounded imitation learning.
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Y6LzLWXlS8E.WNev_iSes.00039
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Section
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Y6LzLWXlS8E_04_00_00
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Section
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WNev_iSes_04_00_00
| 4
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2.1 Imitation learning
|
2.1 Imitation learning
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WNev_iSes_04_00_00
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Imitation learning learns a policy from a dataset of expert demonstrations via supervised learning.
|
Imitation learning learns a policy from a dataset of expert demonstrations via supervised learning.
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WNev_iSes_04_00_01
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The expert is a policy that acts in a (reward-free)
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The expert is a policy that acts in a (reward-free)
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WNev_iSes_04_00_02
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Markov decision process (MDP) defined by a tuple M = ( S , A , P ( s ′ | s, a ) , P ( s 0 )) , where S is the set of states, A is the set of actions, P ( s ′ | s, a ) isthe transition probability, and P ( s 0 ) is a distribution over initial states.
|
Markov decision process (MDP) defined by a tuple M = ( S , A , P ( s ′ | s, a ) , P ( s 0 )) , where S is the set of states, A is the set of actions, P ( s ′ | s, a ) is the transition probability, and P ( s 0 ) is a distribution over initial states.
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WNev_iSes_04_00_03
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The expert’s interaction withthe environment produces a trajectory τ =
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The expert’s interaction with the environment produces a trajectory τ =
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( s 0 , a 0 , . .
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( s 0 , a 0 , . .
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WNev_iSes_04_00_05
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. , a T − 1 , s T ) .
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. , a T − 1 , s T ) .
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WNev_iSes_04_00_06
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The expert may maximize theexpectation over some reward function, but this is not necessary (and some tasks cannot be expressedthrough Markov rewards Abel et al.
|
The expert may maximize the expectation over some reward function, but this is not necessary (and some tasks cannot be expressed through Markov rewards Abel et al.
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WNev_iSes_04_01_00
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In the simplest form of imitation learning, a behavioralcloning policy π η ( a | s ) parametrized by η is learned by minimizing the loss − (cid:80) s,a ∈D log π η ( a | s ) ,where D is the dataset of state-action pairs collected by the expert’s policy.
|
In the simplest form of imitation learning, a behavioral cloning policy π η ( a | s ) parametrized by η is learned by minimizing the loss − (cid:80) s,a ∈D log π η ( a | s ) , where D is the dataset of state-action pairs collected by the expert’s policy.
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WNev_iSes
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Y6LzLWXlS8E.WNev_iSes.00048
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Section
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Y6LzLWXlS8E_05_00_00
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Section
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WNev_iSes_05_00_00
| 5
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2.2 Confounded imitation learning
|
2.2 Confounded imitation learning
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We now extend the imitation learning setup to allow for some variables θ ∈ Θ that are observed bythe expert, but not the imitator.
|
We now extend the imitation learning setup to allow for some variables θ ∈ Θ that are observed by the expert, but not the imitator.
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We define a family of Markov Decision processes as a latent space Θ ,a distribution P ( θ ) , and for each θ ∈ Θ , a reward-free MDP M θ = ( S , A , P ( s ′ | s, a, θ ) , P ( s 0 | θ )) .
|
We define a family of Markov Decision processes as a latent space Θ , a distribution P ( θ ) , and for each θ ∈ Θ , a reward-free MDP M θ = ( S , A , P ( s ′ | s, a, θ ) , P ( s 0 | θ )) .
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We assume there exists an expert policy π exp ( a | s, θ ) for each MDP.
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We assume there exists an expert policy π exp ( a | s, θ ) for each MDP.
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When it interacts with theenvironment, it generates the following distribution over trajectories τ :
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When it interacts with the environment, it generates the following distribution over trajectories τ :
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Y6LzLWXlS8E.WNev_iSes.00053
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Equation
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Y6LzLWXlS8E_05_02_00
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Equation
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WNev_iSes_05_02_00
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[Equation]
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[Equation]
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The imitator does not observe the latent θ .
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The imitator does not observe the latent θ .
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It may thus need to implicitly infer it from the pasttransitions, so we take it to be a non-Markovian policy π η ( a t | s 1 , a 1 , . . .
|
It may thus need to implicitly infer it from the past transitions, so we take it to be a non-Markovian policy π η ( a t | s 1 , a 1 , . . .
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, s t ) , parameterized by η .
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, s t ) , parameterized by η .
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The imitator generates the following distribution over trajectories:
|
The imitator generates the following distribution over trajectories:
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[Equation]
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[Equation]
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The Bayesian networks associated to these distributions are shown in figure 1.
|
The Bayesian networks associated to these distributions are shown in Figure 1.
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The goal of imitation learning in this setting is to learn imitator parameters η such that when theimitator is executed in the environment, the imitator agrees with the expert’s decisions, meaning wewish to maximise
|
The goal of imitation learning in this setting is to learn imitator parameters η such that when the imitator is executed in the environment, the imitator agrees with the expert’s decisions, meaning we wish to maximise
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"8": null,
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00061
| 7
| 0
| 7
| 0
|
62
| 1
|
Equation
|
Y6LzLWXlS8E_05_08_00
| 5
| 2
|
Equation
|
WNev_iSes_05_08_00
| 5
|
[Equation]
|
[Equation]
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00062
| 8
| 0
| 8
| 0
|
63
| 1
|
Paragraph
|
Y6LzLWXlS8E_05_09_00
| 5
| 2
|
Paragraph
|
WNev_iSes_05_09_00
| 5
|
If the expert solves some task (e. g. maximizes some reward function), this amounts to solving thesame task.
|
If the expert solves some task (e. g. maximizes some reward function), this amounts to solving the same task.
|
{
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00063
| 9
| 0
| 9
| 0
|
64
| 2
|
Section
|
Y6LzLWXlS8E_06_00_00
| 6
| 2
|
Section
|
WNev_iSes_06_00_00
| 6
|
2.3 Naive behavioral cloning
|
2.3 Naive behavioral cloning
|
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Y6LzLWXlS8E
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WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00064
| null | null | null | null |
65
| 2
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Paragraph
|
Y6LzLWXlS8E_06_00_00
| 6
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|
Paragraph
|
WNev_iSes_06_00_00
| 6
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If we have access to a data set of expert demonstrations, one can learn an imitator via behavioralcloning on the expert’s demonstrations.
|
If we have access to a data set of expert demonstrations, one can learn an imitator via behavioral cloning on the expert’s demonstrations.
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00065
| 0
| 0
| 0
| 0
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66
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Paragraph
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Y6LzLWXlS8E_06_00_01
| 6
| 2
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Paragraph
|
WNev_iSes_06_00_01
| 6
|
At optimality, this learns the conditional policy :
|
At optimality, this learns the conditional policy :
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00066
| 0
| 1
| 0
| 1
|
67
| 2
|
Equation
|
Y6LzLWXlS8E_06_01_00
| 6
| 2
|
Equation
|
WNev_iSes_06_01_00
| 6
|
[Equation]
|
[Equation]
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00067
| 1
| 0
| 1
| 0
|
68
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_02_00
| 6
| 2
|
Paragraph
|
WNev_iSes_06_02_00
| 6
|
Following Ortega et al.
|
Following Ortega et al.
|
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|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00068
| 2
| 0
| 2
| 0
|
69
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_02_01
| 6
| 2
|
Paragraph
|
WNev_iSes_06_02_01
| 6
|
[2021], consider the following example of a confounded multi-armed banditwith
|
[2021], consider the following example of a confounded multi-armed bandit with A =
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00069
| 2
| 1
| 2
| 1
|
70
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_02_02
| 6
| 2
|
Paragraph
|
WNev_iSes_06_02_02
| 6
|
A = Θ = { 1 , . .
|
Θ = { 1 , . .
|
{
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0,
3
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"8": null,
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00070
| 2
| 2
| 2
| 2
|
71
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_02_03
| 6
| 2
|
Paragraph
|
WNev_iSes_06_02_03
| 6
|
, 5 } and S = { 0 , 1 } :
|
, 5 } and S = { 0 , 1 } :
|
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00071
| 2
| 3
| 2
| 3
|
72
| 2
|
Equation
|
Y6LzLWXlS8E_06_03_00
| 6
| 2
|
Equation
|
WNev_iSes_06_03_00
| 6
|
[Equation]
|
[Equation] [Equation]
|
{
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11,
21
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"intention": "Format"
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}
|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00072
| 3
| 0
| 3
| 0
|
73
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_04_00
| 6
| 2
|
Paragraph
|
WNev_iSes_06_05_00
| 6
|
The expert knows which bandit arm is special (and labeled by θ ) and pulls it with high probability,while the imitating agent does not have access to this information.
|
The expert knows which bandit arm is special (and labeled by θ ) and pulls it with high probability, while the imitating agent does not have access to this information.
|
{
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"sentence-2-token-indices": [
88,
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],
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|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00073
| 4
| 0
| 5
| 0
|
74
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_05_00
| 6
| 2
|
Paragraph
|
WNev_iSes_06_06_00
| 6
|
If we roll out the naive behavioral cloning policy in this environment, shown in Figure 2, we see thecausal delusion at work.
|
If we roll out the naive behavioral cloning policy in this environment, shown in Figure 2, we see the causal delusion at work.
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00074
| 5
| 0
| 6
| 0
|
75
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_05_01
| 6
| 2
|
Paragraph
|
WNev_iSes_06_06_01
| 6
|
At time t , the latent that is inferred by p cond takes past actions as evidencefor the latent variable.
|
At time t , the latent that is inferred by p cond takes past actions as evidence for the latent variable.
|
{
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00075
| 5
| 1
| 6
| 1
|
76
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_05_02
| 6
| 2
|
Paragraph
|
WNev_iSes_06_06_02
| 6
|
This makes sense on the expert demonstrations, as the expert is cognizantof the latent variable.
|
This makes sense on the expert demonstrations, as the expert is cognizant of the latent variable.
|
{
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64,
76
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|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00076
| 5
| 2
| 6
| 2
|
77
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_05_03
| 6
| 2
|
Paragraph
|
WNev_iSes_06_06_03
| 6
|
However, during an imitator roll-out, the past actions are not evidence of thelatent, as the imitator is blind to it.
|
However, during an imitator roll-out, the past actions are not evidence of the latent, as the imitator is blind to it.
|
{
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75,
86
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|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00077
| 5
| 3
| 6
| 3
|
78
| 2
|
Paragraph
|
Y6LzLWXlS8E_06_05_04
| 6
| 2
|
Paragraph
|
WNev_iSes_06_06_04
| 6
|
Concretely, the imitator will take its first action uniformly andlater tends to repeat that action, as it mistakenly takes the first action to be evidence for the latent.
|
Concretely, the imitator will take its first action uniformly and later tends to repeat that action, as it mistakenly takes the first action to be evidence for the latent.
|
{
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"sentence-1-token-indices": [
62,
70
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"sentence-2-token-indices": [
62,
71
],
"intention": "Improve-grammar-Typo"
},
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|
Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00078
| 5
| 4
| 6
| 4
|
79
| 2
|
Section
|
Y6LzLWXlS8E_07_00_00
| 7
| 2
|
Section
|
WNev_iSes_07_00_00
| 7
|
2.4 Interventional policy
|
2.4 Interventional policy
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00079
| null | null | null | null |
80
| 2
|
Paragraph
|
Y6LzLWXlS8E_07_00_00
| 7
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|
Paragraph
|
WNev_iSes_07_00_00
| 7
|
A solution to this issue is to only take as evidence the data that was actually informed by the latent,which are the transitions.
|
A solution to this issue is to only take as evidence the data that was actually informed by the latent, which are the transitions.
|
{
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96,
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Y6LzLWXlS8E
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WNev_iSes
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Y6LzLWXlS8E.WNev_iSes.00080
| 0
| 0
| 0
| 0
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81
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Paragraph
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Y6LzLWXlS8E_07_00_01
| 7
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Paragraph
|
WNev_iSes_07_00_01
| 7
|
This defines the following imitator policy:
|
This defines the following imitator policy:
|
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Y6LzLWXlS8E
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WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00081
| 0
| 1
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| 1
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82
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|
Equation
|
Y6LzLWXlS8E_07_01_00
| 7
| 2
|
Equation
|
WNev_iSes_07_01_00
| 7
|
[Equation]
|
[Equation]
|
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Y6LzLWXlS8E
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WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00082
| 1
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| 1
| 0
|
83
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Paragraph
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Y6LzLWXlS8E_07_02_00
| 7
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Paragraph
|
WNev_iSes_07_02_00
| 7
|
In a causal framework, that corresponds to treating the choice of past actions as interventions.
|
In a causal framework, that corresponds to treating the choice of past actions as interventions.
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00083
| 2
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| 2
| 0
|
84
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Paragraph
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Y6LzLWXlS8E_07_02_01
| 7
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|
Paragraph
|
WNev_iSes_07_02_01
| 7
|
Inthe notation of the do-calculus [Pearl, 2009], this equals p ( a t | s 1 , do( a 1 ) , s 2 , do( a 2 ) , . . .
|
In the notation of the do-calculus [Pearl, 2009], this equals p ( a t | s 1 , do( a 1 ) , s 2 , do( a 2 ) , . . .
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00084
| 2
| 1
| 2
| 1
|
85
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|
Paragraph
|
Y6LzLWXlS8E_07_02_02
| 7
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|
Paragraph
|
WNev_iSes_07_02_02
| 7
|
, s t ) .
|
, s t ) .
|
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00085
| 2
| 2
| 2
| 2
|
86
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|
Paragraph
|
Y6LzLWXlS8E_07_02_03
| 7
| 2
|
Paragraph
|
WNev_iSes_07_02_03
| 7
|
Thepolicy in equation (5) is therefore known as interventional policy [Ortega et al., 2021].
|
The policy in Equation (5) is therefore known as interventional policy [Ortega et al., 2021].
|
{
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Y6LzLWXlS8E
|
WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00086
| 2
| 3
| 2
| 3
|
87
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|
Section
|
Y6LzLWXlS8E_08_00_00
| 8
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Deconfounding imitation learning
|
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Y6LzLWXlS8E
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WNev_iSes
|
Y6LzLWXlS8E.WNev_iSes.00087
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|
88
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|
Figure
|
Y6LzLWXlS8E_08_00_00
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Figure
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WNev_iSes_07_03_00
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[Figure]
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[Figure]
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Y6LzLWXlS8E_08_01_00
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WNev_iSes_08_00_00
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We now present our theoretical results on how imitation learning can be deconfounded.
|
We now present our theoretical results on how imitation learning can be deconfounded.
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WNev_iSes_08_00_01
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We first showthat the interventional policy is optimal in some sense, before analyzing in which settings it can belearned.
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We first show that the interventional policy is optimal in some sense, before analyzing in which settings it can be learned.
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Section
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Section
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WNev_iSes_09_00_00
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3.1 Optimality of the interventional policy
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3.1 Optimality of the interventional policy
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Y6LzLWXlS8E_09_00_00
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Paragraph
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WNev_iSes_09_00_00
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[Figure] Under some reasonable assumptions, the interventional policy approaches the expert’s policy, as weprove in the appendix 2. [Figure]
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Under some reasonable assumptions, the interventional policy approaches the expert’s policy, as we prove in the Appendix B.
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WNev_iSes_09_01_00
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Theorem 3.1 (Informal) .
|
Theorem 3.1 (Informal) .
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WNev_iSes_09_01_01
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If the interventional inference p int ( θ | τ <t ) approaches the true latent of theenvironment as t → ∞ on the rollouts of π int , and if the expert maximises some reward that is fixedacross all environments, then as t → ∞ , the imitator policy π int ( a t | s ) approaches the expert policy.
|
If the interventional inference p int ( θ | τ <t ) approaches the true latent of the environment as t → ∞ on the rollouts of π int , and if the expert maximises some reward that is fixed across all environments, then as t → ∞ , the imitator policy π int ( a t | s ) approaches the expert policy.
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Y6LzLWXlS8E_09_04_00
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Paragraph
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WNev_iSes_09_02_00
| 9
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Proof.
|
Proof.
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WNev_iSes_09_02_01
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See lemma 2.1 in the appendix.
|
See Lemma 2.1 in the appendix.
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WNev_iSes_09_03_00
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The requirement here means that the transition dynamics must be informative about the latent —we consider latent confounders that manifest in the dynamics, not those that affect only the agentbehavior.
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The requirement here means that the transition dynamics must be informative about the latent — we consider latent confounders that manifest in the dynamics, not those that affect only the agent behavior.
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Y6LzLWXlS8E.WNev_iSes.00098
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Y6LzLWXlS8E_09_05_01
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WNev_iSes_09_03_01
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In this case, the interventional policy thus presents a solution to the confounding problem.
|
In this case, the interventional policy thus presents a solution to the confounding problem.
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Y6LzLWXlS8E_09_06_00
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Paragraph
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WNev_iSes_09_04_00
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In the rest of this paper we focus on the question if and how it can be learned from data.
|
In the rest of this paper we focus on the question if and how it can be learned from data.
|
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End of preview.
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