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Title: Single Episode Policy Transfer in Reinforcement Learning

Paper content:
Transfer and adaptation to new unknown environmental dynamics is a key challenge for reinforcement learning (RL).
An even greater challenge is performing near-optimally in a single attempt at test time, possibly without access to dense rewards, which is not addressed by current methods that require multiple experience rollouts for adaptation.
To achieve single episode transfer in a family of environments with related dynamics, we propose a general algorithm that optimizes a probe and an inference model to rapidly estimate underlying latent variables of test dynamics, which are then immediately used as input to a universal control policy.
This modular approach enables integration of state-of-the-art algorithms for variational inference or RL.
Moreover, our approach does not require access to rewards at test time, allowing it to perform in settings where existing adaptive approaches cannot.
In diverse experimental domains with a single episode test constraint, our method significantly outperforms existing adaptive approaches and shows favorable performance against baselines for robust transfer.
One salient feature of human intelligence is the ability to perform well in a single attempt at a new task instance, by recognizing critical characteristics of the instance and immediately executing appropriate behavior based on experience in similar instances.
Artificial agents must do likewise in applications where success must be achieved in one attempt and failure is irreversible.
This problem setting, single episode transfer, imposes a challenging constraint in which an agent experiences-and is evaluated on-only one episode of a test instance.
As a motivating example, a key challenge in precision medicine is the uniqueness of each patient's response to therapeutics (Hodson, 2016; Bordbar et al., 2015; Whirl-Carrillo et al., 2012) .
Adaptive therapy is a promising approach that formulates a treatment strategy as a sequential decision-making problem (Zhang et al., 2017; West et al., 2018; Petersen et al., 2019) .
However, heterogeneity among instances may require explicitly accounting for factors that underlie individual patient dynamics.
For example, in the case of adaptive therapy for sepsis (Petersen et al., 2019) , predicting patient response prior to treatment is not possible.
However, differences in patient responses can be observed via blood measurements very early after the onset of treatment (Cockrell and An, 2018) .
As a first step to address single episode transfer in reinforcement learning (RL), we propose a general algorithm for near-optimal test-time performance in a family of environments where differences in dynamics can be ascertained early during an episode.
Our key idea is to train an inference model and a probe that together achieve rapid inference of latent variables-which account for variation in a family of similar dynamical systems-using a small fraction (e.g., 5%) of the test episode, then deploy a universal policy conditioned on the estimated parameters for near-optimal control on the new instance.
Our approach combines the advantages of robust transfer and adaptation-based transfer, as we learn a single universal policy that requires no further training during test, but which is adapted to the new environment by conditioning on an unsupervised estimation of new latent dynamics.
In contrast to methods that quickly adapt or train policies via gradients during test but assume access to multiple test rollouts and/or dense rewards (Finn et al., 2017; Killian et al., 2017; Rakelly et al., 2019) , we explicitly optimize for performance in one test episode without accessing the reward function at test time.
Hence our method applies to real-world settings in which rewards during test are highly delayed or even completely inaccessible-e.g., a reward that depends on physiological factors that are accessible only in simulation and not from real patients.
We also consider computation time a crucial factor for real-time application, whereas some existing approaches require considerable computation during test (Killian et al., 2017) .
Our algorithm builds on variational inference and RL as submodules, which ensures practical compatibility with existing RL workflows.
Our main contribution is a simple general algorithm for single episode transfer in families of environments with varying dynamics, via rapid inference of latent variables and immediate execution of a universal policy.
Our method attains significantly higher cumulative rewards, with orders of magnitude faster computation time during test, than the state-of-the-art model-based method (Killian et al., 2017) , on benchmark high-dimensional domains whose dynamics are discontinuous and continuous in latent parameters.
We also show superior performance over optimization-based meta-learning and favorable performance versus baselines for robust transfer.
2D navigation and Acrobot are solved upon attaining terminal reward of 1000 and 10, respectively.
SEPT outperforms all baselines in 2D navigation and takes significantly fewer number of steps to solve (Figures 2a and 2c) .
While a single instance of 2D navigation is easy for RL, handling multiple instances is highly non-trivial.
EPOpt-adv and Avg almost never solve the test instance-we set "steps to solve" to 50 for test episodes that were unsolved-because interpolating between instance-specific optimal policies in policy parameter space is not meaningful for any task instance.
MAML did not perform well despite having the advantage of being provided with rewards at test time, unlike SEPT.
The gradient adaptation step was likely ineffective because the rewards are sparse and delayed.
BNN requires significantly more steps than SEPT, and it uses four orders of magnitude longer computation time (Table 4) , due to training a policy from scratch during the test episode.
Training times of all algorithms except BNN are in the same order of magnitude (Table 3) .
In Acrobot and HIV, where dynamics are continuous in latent variables, interpolation within policy space can produce meaningful policies, so all baselines are feasible in principle.
SEPT is statistically significantly faster than BNN and Avg, is within error bars of MAML, while EPOpt-adv outperforms the rest by a small margin (Figures 2b and 2d ).
Figure 5 shows that SEPT is competitive in terms of percentage of solved instances.
As the true values of latent variables for Acrobot test instances were interpolated and extrapolated from the training values, this shows that SEPT is robust to out-oftraining dynamics.
BNN requires more steps due to simultaneously learning and executing control during the test episode.
On HIV, SEPT reaches significantly higher cumulative rewards than all methods.
Oracle is within the margin of error of Avg.
This may be due to insufficient examples of the high-dimensional ground truth hidden parameters.
Due to its long computational time, we run three seeds for BNN on HIV, shown in Figure 4b , and find it was unable to adapt within one test episode.
Comparing directly to reported results in DPT (Yao et al., 2018) , SEPT solves 2D Navigation at least 33% (>10 steps) faster, and the cumulative reward of SEPT (mean and standard error) are above DPT's mean cumulative reward in Acrobot (Table 2) .
Together, these results show that methods that explicitly distinguish different dynamics (e.g., SEPT and BNN) can significantly outperform methods that implicitly interpolate in policy parameter space (e.g., Avg and EPOpt-adv) in settings where z has large discontinuous effect on dynamics, such as 2D navigation.
When dynamics are continuous in latent variables (e.g., Acrobot and HIV), interpolation-based methods fare better than BNN, which faces the difficulty of learning a model of the entire family of dynamics.
SEPT worked the best in the first case and is robust to the second case because it explicitly distinguishes dynamics and does not require learning a full transition model.
Moreover, SEPT does not require rewards at test time allowing it be useful on a broader class of problems than optimization-based meta-learning approaches like MAML.
Appendix D contains training curves.
Figures 2f, 2g and 2j show that the probe phase is necessary to solve 2D navigation quickly, while giving similar performance in Acrobot and significant improvement in HIV.
SEPT significantly outperformed TotalVar in 2D navigation and HIV, while TotalVar gives slight improvement in Acrobot, showing that directly using VAE performance as the reward for probing in certain environments can be more effective than a reward that deliberately encourages perturbation of state dimensions.
The clear advantage of SEPT over MaxEnt in 2D navigation and HIV supports our hypothesis in Section 3.3 that the variational lowerbound, rather than its negation in the maximum entropy viewpoint, should be used as the probe reward, while performance was not significantly differentiated in Acrobot.
SEPT outperforms DynaSEPT on all problems where dynamics are stationary during each instance.
On the other hand, DynaSEPT is the better choice in a non-stationary variant of 2D navigation where the dynamics "switch" abruptly at t = 10 (Figure 4c) .
Figure 3 shows that SEPT is robust to varying the probe length T p and dim(z).
Even with certain suboptimal probe length and dim(z), it can outperform all baselines on 2D navigation in both steps-to-solve and final reward; it is within error bars of all baselines on Acrobot based on final cumulative reward; and final cumulative reward exceeds that of baselines in HIV.
Increasing T p means foregoing valuable steps of the control policy and increasing difficulty of trajectory reconstruction for the VAE in high dimensional state spaces; T p is a hyper-parameter that should be validated for each application.
Appendix D.5 shows the effect of β on latent variable encodings.
We propose a general algorithm for single episode transfer among MDPs with different stationary dynamics, which is a challenging goal with real-world significance that deserves increased effort from the transfer learning and RL community.
Our method, Single Episode Policy Transfer (SEPT), trains a probe policy and an inference model to discover a latent representation of dynamics using very few initial steps in a single test episode, such that a universal policy can execute optimal control without access to rewards at test time.
Strong performance versus baselines in domains involving both continuous and discontinuous dependence of dynamics on latent variables show the promise of SEPT for problems where different dynamics can be distinguished via a short probing phase.
The dedicated probing phase may be improved by other objectives, in addition to performance of the inference model, to mitigate the risk and opportunity cost of probing.
An open challenge is single episode transfer in domains where differences in dynamics of different instances are not detectable early during an episode, or where latent variables are fixed but dynamics are nonstationary.
Further research on dynamic probing and control, as sketched in DynaSEPT, is one path toward addressing this challenge.
Our work is one step along a broader avenue of research on general transfer learning in RL equipped with the realistic constraint of a single episode for adaptation and evaluation.
A DERIVATIONS Proposition 1.
Let p ϕ (τ ) denote the distribution of trajectories induced by π ϕ .
Then the gradient of the entropy H(p ϕ (τ )) is given by
Proof.
Assuming regularity, the gradient of the entropy is
For trajectory τ := (s 0 , a 0 , s 1 , . . . , s t ) generated by the probe policy π ϕ :
Since p(s 0 ) and p(s i+1 |s i , a i ) do not depend on ϕ, we get
Substituting this into the gradient of the entropy gives equation 3.
Restore trained decoder ψ, encoder φ, probe policy ϕ, and control policy θ 3:

assistant: text: Single episode policy transfer in a family of environments with related dynamics, via optimized probing for rapid inference of latent variables and immediate execution of a universal policy.