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md/train/SkfTIj0cKX/SkfTIj0cKX.md

@@ -70,9 +70,9 @@ In A3C multiple agents interact in parallel, with multiple instances of the envi
 In this section we incorporate the imagination reconstruction module into the model-free agents (e.g., A3C) in order to enhance data efficiency, promote more robust learning and ultimately higher performance under the sparse extrinsic reward. Our IRN implements an imagination-augmented policy via three key components (Figure 2). The imagination core $( I C )$ predicts the next time steps conditioned on actions sampled from the imagination policy $\hat { \pi }$ . At a time step $t$ , the trajectory manager (TM) determines how to roll out the $I C$ under the planning strategy, and then produces imagined trajectories $\hat { T _ { 1 } } , \dots , \hat { T _ { n } }$ of an observable world state $s _ { t }$ . Each trajectory $\hat { T _ { j } }$ is a sequence of items $\{ \hat { i } _ { j , t } , \hat { i } _ { j , t + 1 } , \ldots \}$ , that users may purchase (or click) from the current time $t$ . The Imaginationaugmented Executor $( I A E )$ aggregates the internal data resulting from imagination and external rewarding data to update its action policy $\pi$ . Specifically, the $I A E$ optimizes the policy $\pi$ by maximizing the extrinsic reward while minimizing the intrinsic imagination error. In principle, IRN encourages exploration and learns predictive representations via imagination rollouts, which promotes quick adaptation to user interest and robustness to the cold-start scenario.
 
 ![](images/f8520ca08c0f83e6c0e4b54ca0deec2292206bd1595905e810a70095d85f4835.jpg)  
-ˆit+⌧ = ˆat+⌧ and sˆt = st , where ⌧ is the length of the imagined rollout, aˆt+⌧ the4agination policy ⇡ˆ. During training, the generated i28 32 31 example, [23] adopted Markov chain toning, the generated item ˆit+⌧ may not be the true puFigure 2: IRN architecture: a) the imagination core $( I C )$ action of theˆit+⌧ may not be the true purchase, but we24 aT 1 28 purchase.chase.any real-world applications, users’ current interests are inel user behavior sequences, and [19, 31] leveragedse, but wepredicts the next time step and then generates imagination policy ⇡ˆ. During training,still use it for self-supervised reconstrill use it for self-supervis32 recurr33 prediconstruction of I2E. This mdistillation [] or fixed targthe imagined trajectories $\hat { \tau }$ errorgenerated item it+⌧ may not be the true purchase, but weon of I2E. This makes the action policy ⇡ more robust to reconstruction of I2E. This makes the action policy ⇡ more robust to25 ⇡, V 30 e.g., sequential r29 Compared with state-of-the-art methods that consider users’ se33        neural networks (RNNs) to embed previously purchased products for current interest.kes the action policy ⇡ more robust toetworkˆ; b) the trajectory manager (TM) employs various planning strategies (e.g., intrinsictrinsicginatio  depth- $\mathbf { \nabla } m$ rs and forces the imagination policy ⇡ˆ to generate moors and forces the imagination popolicy ⇡ˆ to generate more accurat   t here) to control the granularity of $\dot { \mathcal { T } }$ ccurate actions.y ⇡ˆ to generate more accurate actions.26 session-based recom32 In many real-w30 e.g., sequential recommenders with recurrent neural networksSubmitted to 32nd Conference on Neural Information Processing Sysctions.; c) the imagination-augmented executor (IAE) optimizes In practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target networklike DQN []. The former distills the action policy ⇡(s ; ✓) into a smaller rollout network ⇡ˆ(s ; ˆ ✓),practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target netwo27  28 purchase.33 To m      Submitted to 32nd Conference on Neural Information Processing Systems (NIPS 2018). Do not distribute.⇡ˆ can be obtained from policy distillation [] or fixed target network The latter uses a shared but slowlythe network using the internal imagination data and external rewarding data (e.g., purchases).
+ˆit+⌧ = ˆat+⌧ and sˆt = st , where ⌧ is the length of the imagined rollout, aˆt+⌧ the4agination policy ⇡ˆ. During training, the generated i28 32 31 example, [23] adopted Markov chain toning, the generated item ˆit+⌧ may not be the true puFigure 2: IRN architecture: a) the imagination core $( I C )$ action of theˆit+⌧ may not be the true purchase, but we24 aT 1 28 purchase.chase.any real-world applications, users’ current interests are inel user behavior sequences, and [19, 31] leveragedse, but wepredicts the next time step and then generates imagination policy ⇡ˆ. During training,still use it for self-supervised reconstrill use it for self-supervis32 recurr33 prediconstruction of I2E. This mdistillation [] or fixed targthe imagined trajectories $\hat { \tau }$ errorgenerated item it+⌧ may not be the true purchase, but weon of I2E. This makes the action policy ⇡ more robust to reconstruction of I2E. This makes the action policy ⇡ more robust to25 ⇡, V 30 e.g., sequential r29 Compared with state-of-the-art methods that consider users’ se33        neural networks (RNNs) to embed previously purchased products for current interest.kes the action policy ⇡ more robust toetworkˆ; b) the trajectory manager (TM) employs various planning strategies (e.g., intrinsictrinsicginatio  depth- $\mathbf { \nabla } m$ rs and forces the imagination policy ⇡ˆ to generate moors and forces the imagination popolicy ⇡ˆ to generate more accurat   t here) to control the granularity of $\dot { \mathcal { T } }$ ccurate actions.y ⇡ˆ to generate more accurate actions.26 session-based recom32 In many real-w30 e.g., sequential recommenders with recurrent neural networksSubmitted to 32nd Conference on Neural Information Processing Sysctions.; c) the imagination-augmented executor (IAE) optimizes In practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target networklike DQN []. The former distills the action policy ⇡(s ; ✓) into a smaller rollout network ⇡ˆ(s ; ˆ ✓),practice, the imagination policy ⇡ˆ can be obtained from policy distillation [] or fixed target netwo27  28 purchase.33 To m      Submitted to 32nd Conference on Neural Information Processing Systems (NIPS 2018). Do not distribute.⇡ˆ can be obtained from policy distillation [] or fixed target network The latter uses a shared but slowlythe network using the internal imagination data and external rewarding data (e.g., purchases).
 
-ot+1this also helps I2E learn a predictive representation of rewarding states, and in turn should allow the anging target network ⇡ˆ(s ; ✓), where ✓ are previous parameters in ⇡(s ; ✓). By imitating theSubmitted to 32nd Conference on Neural Information Processing Sy ), where ✓ are previous parameters in ⇡(s ; ✓). By imitating theImagination Core In order to simulate imagined trajectories, we rely on environment models that, Sttion policy ⇡, the imagined trajectories will be similar to agent experiences in the real environment;33 To model this phenomctories will be similar to agent experiences in the real environment;given the present state and a candidate action, make predictions about the future states. In general, 2 IRN do not predict the rewards, since it is not useful as reported in []. and in RS, rewards of different actionsis also helps I2E learn a predictive representation of rewarding states, and in turn should allow theive representation of rewarding states, and in turn should allow thewe can employ an environment model that build on action-conditional next-step predictors (Oh et al., ot+2are hard to specifysy learning of the action policy under the sparse reward signals. Submitted to 32nd Confe under the sparse reward signals.       2015), and train it in an unsupervised fashion from agent experiences. However, the predictors usually 4suffer from model errors, resulting in poor agent performance, and require extra computational cost 2(e.g., pre-training). Besides, the predictors may learn a trivial identical function, since the state e hard to specify transition in agent trajectories (or session data) is deterministic, i.e., $s _ { t + 1 } = s _ { t } \cup \{ i _ { t } \}$ and $i _ { t } = a _ { t }$ . In this work, we derive a static environment model from the state transition: $\hat { s } _ { t + \tau + 1 } = \hat { s } _ { t + \tau } \cup \{ \hat { i } _ { t + \tau } \}$ , $\hat { i } _ { t + \tau } = \hat { a } _ { t + \tau }$ and $\hat { s } _ { t } = s _ { t }$ , where $\tau$ is the length of the imagined rollout, $\hat { a } _ { t + \tau }$ the output action of the imagination policy $\hat { \pi }$ . During training, the generated item $\hat { i } _ { t + \tau }$ may not be the true purchase/click, RLAgentbut we still use it for self-supervised reconstruction. This makes the action policy $\pi$ more robust to intrinsic errors and forces the imagination policy $\hat { \pi }$ to generate more accurate actions.
+ot+1this also helps I2E learn a predictive representation of rewarding states, and in turn should allow the anging target network ⇡ˆ(s ; ✓), where ✓ are previous parameters in ⇡(s ; ✓). By imitating theSubmitted to 32nd Conference on Neural Information Processing Sy ), where ✓ are previous parameters in ⇡(s ; ✓). By imitating theImagination Core In order to simulate imagined trajectories, we rely on environment models that, Sttion policy ⇡, the imagined trajectories will be similar to agent experiences in the real environment;33 To model this phenomctories will be similar to agent experiences in the real environment;given the present state and a candidate action, make predictions about the future states. In general, 2 IRN do not predict the rewards, since it is not useful as reported in []. and in RS, rewards of different actionsis also helps I2E learn a predictive representation of rewarding states, and in turn should allow theive representation of rewarding states, and in turn should allow thewe can employ an environment model that build on action-conditional next-step predictors (Oh et al., ot+2are hard to specifysy learning of the action policy under the sparse reward signals. Submitted to 32nd Confe under the sparse reward signals.       2015), and train it in an unsupervised fashion from agent experiences. However, the predictors usually 4suffer from model errors, resulting in poor agent performance, and require extra computational cost 2(e.g., pre-training). Besides, the predictors may learn a trivial identical function, since the state e hard to specify transition in agent trajectories (or session data) is deterministic, i.e., $s _ { t + 1 } = s _ { t } \cup \{ i _ { t } \}$ and $i _ { t } = a _ { t }$ . In this work, we derive a static environment model from the state transition: $\hat { s } _ { t + \tau + 1 } = \hat { s } _ { t + \tau } \cup \{ \hat { i } _ { t + \tau } \}$ , $\hat { i } _ { t + \tau } = \hat { a } _ { t + \tau }$ and $\hat { s } _ { t } = s _ { t }$ , where $\tau$ is the length of the imagined rollout, $\hat { a } _ { t + \tau }$ the output action of the imagination policy $\hat { \pi }$ . During training, the generated item $\hat { i } _ { t + \tau }$ may not be the true purchase/click, RLAgentbut we still use it for self-supervised reconstruction. This makes the action policy $\pi$ more robust to intrinsic errors and forces the imagination policy $\hat { \pi }$ to generate more accurate actions.
 
 In practice, the imagination policy $\hat { \pi }$ v1can be obtained from policy distillation (Racanière et al., 2017) or a fixed target network like DQN (Mnih et al., 2015). The former distills the action policy $\pi ( s _ { t } ; \theta )$ into a smaller rollout network $\hat { \pi } ( s _ { t } ; \hat { \theta } )$ , using a cross-entropy loss, $\begin{array} { r } { l _ { \pi , \hat { \pi } } ( s _ { t } ) = \sum _ { a } \pi ( a | s _ { t } ) l o g \hat { \pi } ( a | s _ { t } ; \hat { \theta } ) } \end{array}$ . The latter uses a shared but slowly changing network $\hat { \pi } ( s _ { t } ; \theta ^ { - } )$ , where $\theta ^ { - }$ are previous parameters in $\pi ( s _ { t } ; \theta )$ . By imitating the action policy $\pi$ , the imagined trajectories will be similar to agent experiences in the real environment; this also helps $I A E$ learn predictive representations of rewarding states, and in turn should allow the easy learning of the action policy under the sparse reward signals.
 

md/train/VRgITLy0l2/VRgITLy0l2.md

@@ -66,7 +66,7 @@ $$
 \frac { d E } { d t } \leq - k _ { \operatorname* { m i n } } \gamma E ^ { \beta }
 $$
 
-where $\begin{array} { r } { k _ { \operatorname* { m i n } } = \operatorname* { m i n } ( k _ { i } ) , i = 1 , 2 , \cdots , n , \beta = \frac { \alpha } { \alpha + 1 } } \end{array}$ = αα+1 and |e¯|α = |e¯|α+1
 αα+1 = Eβ has been utilized. Noting that $E$ is a positive definite function and scalars $k _ { \mathrm { m i n } }$ and $\gamma$ are always positive, the proof is complete by applying (Bhat & Bernstein, 2000, Theorem 4.2). □
+where $\begin{array} { r } { k _ { \operatorname* { m i n } } = \operatorname* { m i n } ( k _ { i } ) , i = 1 , 2 , \cdots , n , \beta = \frac { \alpha } { \alpha + 1 } } \end{array}$ = αα+1 and |e¯|α = |e¯|α+1
 αα+1 = Eβ has been utilized. Noting that $E$ is a positive definite function and scalars $k _ { \mathrm { m i n } }$ and $\gamma$ are always positive, the proof is complete by applying (Bhat & Bernstein, 2000, Theorem 4.2). □
 
 # 2.2 MULTI NEURON CASE