File size: 8,109 Bytes
fc0f7bd | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 | # Copyright 2024 DeepMind Technologies Limited. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for `linesearch.py`."""
import functools
import itertools
import math
from absl.testing import absltest
from absl.testing import parameterized
import chex
import jax
import jax.numpy as jnp
import jax.random as jrd
import numpy as np
from optax._src import alias
from optax._src import combine
from optax._src import linesearch
from optax._src import update
from optax._src import utils
import optax.tree_utils as optax_tu
class BacktrackingLinesearchTest(chex.TestCase):
def get_fun(self, name):
"""Common ill-behaved functions."""
def rosenbrock(x):
return jnp.sum(100.0 * jnp.diff(x) ** 2 + (1.0 - x[:-1]) ** 2)
def himmelblau(x):
return (x[0] ** 2 + x[1] - 11.0) ** 2 + (x[0] + x[1] ** 2 - 7.0) ** 2
def matyas(x):
return 0.26 * (x[0] ** 2 + x[1] ** 2) - 0.48 * x[0] * x[1]
def eggholder(x):
return -(x[1] + 47) * jnp.sin(
jnp.sqrt(jnp.abs(x[0] / 2.0 + x[1] + 47.0))
) - x[0] * jnp.sin(jnp.sqrt(jnp.abs(x[0] - (x[1] + 47.0))))
funs = dict(
rosenbrock=rosenbrock,
himmelblau=himmelblau,
matyas=matyas,
eggholder=eggholder,
)
return funs[name]
def check_decrease_conditions(
self, fun, init_params, descent_dir, final_params, final_state, opt_args
):
"""Check decrease conditions."""
init_value, init_grad = jax.value_and_grad(fun)(init_params)
final_value = fun(final_params)
final_lr = final_state[0]
slope = optax_tu.tree_vdot(descent_dir, init_grad)
slope_rtol, atol, rtol = (
opt_args['slope_rtol'],
opt_args['atol'],
opt_args['rtol'],
)
sufficient_decrease = (
final_value
<= (1 + rtol) * init_value + slope_rtol * final_lr * slope + atol
)
self.assertTrue(sufficient_decrease)
@chex.all_variants
@parameterized.product(
name_fun_and_init_params=[
('rosenbrock', np.zeros(2)),
('himmelblau', np.ones(2)),
('matyas', np.ones(2) * 6.0),
('eggholder', np.ones(2) * 100.0),
],
increase_factor=[1.0, 1.5, math.inf],
slope_rtol=[1e-4, 0.0],
atol=[1e-4, 0.0],
rtol=[1e-4, 0.0],
)
def test_linesearch_one_step(
self,
name_fun_and_init_params,
increase_factor,
slope_rtol,
atol,
rtol,
):
name_fun, init_params = name_fun_and_init_params
fn = self.get_fun(name_fun)
base_opt = alias.sgd(learning_rate=1.0)
descent_dir = -jax.grad(fn)(init_params)
opt_args = dict(
max_backtracking_steps=30,
slope_rtol=slope_rtol,
increase_factor=increase_factor,
atol=atol,
rtol=rtol,
)
solver = combine.chain(
base_opt,
linesearch.scale_by_backtracking_linesearch(**opt_args),
)
init_state = solver.init(init_params)
update_fn = functools.partial(solver.update, value_fn=fn)
update_fn = self.variant(update_fn)
value, grad = jax.value_and_grad(fn)(init_params)
updates, state = update_fn(
grad, init_state, init_params, value=value, grad=grad
)
params = update.apply_updates(init_params, updates)
self.check_decrease_conditions(
fn, init_params, descent_dir, params, state[-1], opt_args
)
def test_gradient_descent_with_linesearch(self):
init_params = jnp.array([-1.0, 10.0, 1.0])
final_params = jnp.array([1.0, -1.0, 1.0])
def fn(params):
return jnp.sum((params - final_params) ** 2)
# Base optimizer with a large learning rate to see if the linesearch works.
base_opt = alias.sgd(learning_rate=10.0)
solver = combine.chain(
base_opt,
linesearch.scale_by_backtracking_linesearch(max_backtracking_steps=15),
)
init_state = solver.init(init_params)
max_iter = 40
update_fn = functools.partial(solver.update, value_fn=fn)
update_fn = jax.jit(update_fn)
params = init_params
state = init_state
for _ in range(max_iter):
value, grad = jax.value_and_grad(fn)(params)
updates, state = update_fn(grad, state, params, value=value, grad=grad)
params = update.apply_updates(params, updates)
chex.assert_trees_all_close(final_params, params, atol=1e-2, rtol=1e-2)
@chex.variants(
with_jit=True,
without_jit=True,
with_pmap=False,
with_device=True,
without_device=True,
)
def test_recycling_value_and_grad(self):
# A vmap or a pmap makes the cond in value_and_state_from_grad
# become a select and in that case this code cannot be optimal.
# So we skip the pmap test.
init_params = jnp.array([1.0, 10.0, 1.0])
final_params = jnp.array([1.0, -1.0, 1.0])
def fn(params):
return jnp.sum((params - final_params) ** 2)
value_and_grad = utils.value_and_grad_from_state(fn)
base_opt = alias.sgd(learning_rate=0.1)
solver = combine.chain(
base_opt,
linesearch.scale_by_backtracking_linesearch(
max_backtracking_steps=15,
increase_factor=1.0,
slope_rtol=0.5,
store_grad=True,
),
)
init_state = solver.init(init_params)
max_iter = 40
update_fn = functools.partial(solver.update, value_fn=fn)
def fake_fun(_):
return 1.0
fake_value_and_grad = utils.value_and_grad_from_state(fake_fun)
def step_(params, state, iter_num):
# Should still work as the value and grad are extracted from the state
value, grad = jax.lax.cond(
iter_num > 0,
lambda: fake_value_and_grad(params, state=state),
lambda: value_and_grad(params, state=state),
)
updates, state = update_fn(grad, state, params, value=value, grad=grad)
params = update.apply_updates(params, updates)
return params, state
step = self.variant(step_)
params = init_params
state = init_state
for iter_num in range(max_iter):
params, state = step(params, state, iter_num)
params = jax.block_until_ready(params)
chex.assert_trees_all_close(final_params, params, atol=1e-2, rtol=1e-2)
def test_armijo_sgd(self):
def fn(params, x, y):
return jnp.sum((x.dot(params) - y) ** 2)
# Create artificial data
noise = 1e-3
key = jrd.PRNGKey(0)
x_key, y_key, params_key = jrd.split(key, 3)
d, m, n = 2, 16, 2
xs = jrd.normal(x_key, (n, m, d))
target_params = jrd.normal(params_key, (d,))
ys = jnp.stack([x.dot(target_params) for x in xs])
ys = ys + noise * jrd.normal(y_key, (n, m))
xs_iter = itertools.cycle(iter(xs))
ys_iter = itertools.cycle(iter(ys))
init_params = jnp.zeros((d,))
base_opt = alias.sgd(learning_rate=1.0)
solver = combine.chain(
base_opt,
linesearch.scale_by_backtracking_linesearch(max_backtracking_steps=15),
)
num_passes = 10
state = solver.init(init_params)
update_fn = functools.partial(solver.update, value_fn=fn)
update_fn = jax.jit(update_fn)
params = init_params
for _ in range(num_passes):
x, y = next(xs_iter), next(ys_iter)
value, grad = jax.value_and_grad(fn)(params, x, y)
updates, state = update_fn(
grad, state, params, value=value, grad=grad, x=x, y=y
)
params = update.apply_updates(params, updates)
chex.assert_trees_all_close(
params, target_params, atol=5 * 1e-2, rtol=5 * 1e-2
)
if __name__ == '__main__':
absltest.main()
|