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Register a new userBatch Stationary Distribution Estimation
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Junfeng Wen
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. Classical simulation-based approaches assume access to the underlying process so that trajectories of sufficient length can be gathered to approximate stationary sampling. Instead, we consider an alternative setting where a fixed set of transitions has been collected beforehand, by a separate, possibly unknown procedure. The goal is still to estimate properties of the stationary distribution, but without additional access to the underlying system. We propose a consistent estimator that is based on recovering a correction ratio function over the given data. In particular, we develop a variational power method (VPM) that provides provably consistent estimates under general conditions. In addition to unifying a number of existing approaches from different subfields, we also find that VPM yields significantly better estimates across a range of problems, including queueing, stochastic differential equations, post-processing MCMC, and off-policy evaluation.
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Batch normalization (BN) is a technique to normalize activations in intermediate layers of deep neural networks. Its tendency to improve accuracy and speed up training have established BN as a favorite technique in deep learning. Yet, despite its enormous success, there remains little consensus on the exact reason and mechanism behind these improvements. In this paper we take a step towards a better understanding of BN, following an empirical approach. We conduct several experiments, and show that BN primarily enables training with larger learning rates, which is the cause for faster convergence and better generalization. For networks without BN we demonstrate how large gradient updates can result in diverging loss and activations growing uncontrollably with network depth, which limits possible learning rates. BN avoids this problem by constantly correcting activations to be zero-mean and of unit standard deviation, which enables larger gradient steps, yields faster convergence and may help bypass sharp local minima. We further show various ways in which gradients and activations of deep unnormalized networks are ill-behaved. We contrast our results against recent findings in random matrix theory, shedding new light on classical initialization schemes and their consequences.
In batch reinforcement learning (RL), one often constrains a learned policy to be close to the behavior (data-generating) policy, e.g., by constraining the learned action distribution to differ from the behavior policy by some maximum degree that is the same at each state. This can cause batch RL to be overly conservative, unable to exploit large policy changes at frequently-visited, high-confidence states without risking poor performance at sparsely-visited states. To remedy this, we propose residual policies, where the allowable deviation of the learned policy is state-action-dependent. We derive a new for RL method, BRPO, which learns both the policy and allowable deviation that jointly maximize a lower bound on policy performance. We show that BRPO achieves the state-of-the-art performance in a number of tasks.
We tackle the Multi-task Batch Reinforcement Learning problem. Given multiple datasets collected from different tasks, we train a multi-task policy to perform well in unseen tasks sampled from the same distribution. The task identities of the unseen tasks are not provided. To perform well, the policy must infer the task identity from collected transitions by modelling its dependency on states, actions and rewards. Because the different datasets may have state-action distributions with large divergence, the task inference module can learn to ignore the rewards and spuriously correlate $textit{only}$ state-action pairs to the task identity, leading to poor test time performance. To robustify task inference, we propose a novel application of the triplet loss. To mine hard negative examples, we relabel the transitions from the training tasks by approximating their reward functions. When we allow further training on the unseen tasks, using the trained policy as an initialization leads to significantly faster convergence compared to randomly initialized policies (up to $80%$ improvement and across 5 different Mujoco task distributions). We name our method $textbf{MBML}$ ($textbf{M}text{ulti-task}$ $textbf{B}text{atch}$ RL with $textbf{M}text{etric}$ $textbf{L}text{earning}$).
Off-policy learning is a framework for evaluating and optimizing policies without deploying them, from data collected by another policy. Real-world environments are typically non-stationary and the offline learned policies should adapt to these changes. To address this challenge, we study the novel problem of off-policy optimization in piecewise-stationary contextual bandits. Our proposed solution has two phases. In the offline learning phase, we partition logged data into categorical latent states and learn a near-optimal sub-policy for each state. In the online deployment phase, we adaptively switch between the learned sub-policies based on their performance. This approach is practical and analyzable, and we provide guarantees on both the quality of off-policy optimization and the regret during online deployment. To show the effectiveness of our approach, we compare it to state-of-the-art baselines on both synthetic and real-world datasets. Our approach outperforms methods that act only on observed context.
This paper considers batch Reinforcement Learning (RL) with general value function approximation. Our study investigates the minimal assumptions to reliably estimate/minimize Bellman error, and characterizes the generalization performance by (local) Rademacher complexities of general function classes, which makes initial steps in bridging the gap between statistical learning theory and batch RL. Concretely, we view the Bellman error as a surrogate loss for the optimality gap, and prove the followings: (1) In double sampling regime, the excess risk of Empirical Risk Minimizer (ERM) is bounded by the Rademacher complexity of the function class. (2) In the single sampling regime, sample-efficient risk minimization is not possible without further assumptions, regardless of algorithms. However, with completeness assumptions, the excess risk of FQI and a minimax style algorithm can be again bounded by the Rademacher complexity of the corresponding function classes. (3) Fast statistical rates can be achieved by using tools of local Rademacher complexity. Our analysis covers a wide range of function classes, including finite classes, linear spaces, kernel spaces, sparse linear features, etc.
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