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Provable Representation with Efficient Planning for Partial Observable Reinforcement Learning

Hongming Zhang, Tongzheng Ren, Chenjun Xiao, Dale Schuurmans, Bo Dai

TL;DR

The paper tackles reinforcement learning under partial observability by addressing POMDPs with an $L$-decodable structure. It introduces the Multi-step Latent Variable Representation ($\mu$LV-Rep), which yields a linear $Q^\pi$ representation in terms of $p(\cdot|x_h,a_h)$ and enables tractable planning without explicit belief computation. The authors develop a variational latent-variable learning approach to fit $p(\cdot|x_h,a_h)$, combine it with planning (e.g., SAC for continuous actions) and exploration bonuses, and prove PAC-like sample complexity guarantees under realizability and RKHS assumptions. Empirically, $\mu$LV-Rep achieves superior performance on visual, partially observable robotic tasks (Meta-World and partial-observable MuJoCo) compared to strong baselines, approaching or surpassing fully-observed performance in many tasks. The work demonstrates that carefully structured latent representations can yield provably efficient and practical RL for partially observable environments.

Abstract

In most real-world reinforcement learning applications, state information is only partially observable, which breaks the Markov decision process assumption and leads to inferior performance for algorithms that conflate observations with state. Partially Observable Markov Decision Processes (POMDPs), on the other hand, provide a general framework that allows for partial observability to be accounted for in learning, exploration and planning, but presents significant computational and statistical challenges. To address these difficulties, we develop a representation-based perspective that leads to a coherent framework and tractable algorithmic approach for practical reinforcement learning from partial observations. We provide a theoretical analysis for justifying the statistical efficiency of the proposed algorithm, and also empirically demonstrate the proposed algorithm can surpass state-of-the-art performance with partial observations across various benchmarks, advancing reliable reinforcement learning towards more practical applications.

Provable Representation with Efficient Planning for Partial Observable Reinforcement Learning

TL;DR

The paper tackles reinforcement learning under partial observability by addressing POMDPs with an -decodable structure. It introduces the Multi-step Latent Variable Representation (LV-Rep), which yields a linear representation in terms of and enables tractable planning without explicit belief computation. The authors develop a variational latent-variable learning approach to fit , combine it with planning (e.g., SAC for continuous actions) and exploration bonuses, and prove PAC-like sample complexity guarantees under realizability and RKHS assumptions. Empirically, LV-Rep achieves superior performance on visual, partially observable robotic tasks (Meta-World and partial-observable MuJoCo) compared to strong baselines, approaching or surpassing fully-observed performance in many tasks. The work demonstrates that carefully structured latent representations can yield provably efficient and practical RL for partially observable environments.

Abstract

In most real-world reinforcement learning applications, state information is only partially observable, which breaks the Markov decision process assumption and leads to inferior performance for algorithms that conflate observations with state. Partially Observable Markov Decision Processes (POMDPs), on the other hand, provide a general framework that allows for partial observability to be accounted for in learning, exploration and planning, but presents significant computational and statistical challenges. To address these difficulties, we develop a representation-based perspective that leads to a coherent framework and tractable algorithmic approach for practical reinforcement learning from partial observations. We provide a theoretical analysis for justifying the statistical efficiency of the proposed algorithm, and also empirically demonstrate the proposed algorithm can surpass state-of-the-art performance with partial observations across various benchmarks, advancing reliable reinforcement learning towards more practical applications.
Paper Structure (33 sections, 10 theorems, 54 equations, 7 figures, 3 tables, 2 algorithms)

This paper contains 33 sections, 10 theorems, 54 equations, 7 figures, 3 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Difficulties in Learning with POMDPs
  4. Multi-step Latent Variable Representation
  5. Efficient Policy Evaluation from Key Observations
  6. Belief Elimination.
  7. Linear Representation for $Q^\pi$.
  8. Remark (Identifiability):
  9. Least Square Policy Evaluation.
  10. Remark (Connection to Linear MDPs jin2020provablyyang2020reinforcement):
  11. Remark (Connection to PSR littman2001predictive:
  12. Learning with Exploration
  13. Variational Learning of $\mu$LV-Rep.
  14. Practical Parametrization of $Q^\pi$ with $\mu$LV-Rep.
  15. Planning and Exploration with $\mu$LV-Rep.
  16. ...and 18 more sections

Key Result

Theorem 3

Assume the kernel $K$ satisfies the regularity conditions in Appendix sec:technical_conditions. If we properly choose the exploration bonus $\hat{b}_k(x, a)$, we can obtain an $\varepsilon$-optimal policy with probability at least $1-\delta$ after we interact with the environments for $N = \mathrm{p

Figures (7)

  • Figure 1: Learning curves on visual robotic manipulation tasks from Meta-world measured by success rate. Our method shows better or comparable sample efficiency compared to baseline methods. Learning curves on all 50 tasks are reported in \ref{['sec:imp detail']}.
  • Figure 2: The performance gain on 50 Meta-world tasks after 1 million interactions. Our results surpass or are comparable to (with a difference of less than or equal to 10%) the best baselines on 41 out of the 50 tasks.
  • Figure 3: Visualization of the visual robotic manipulation tasks in Meta-world.
  • Figure 4: Visualization of the visual control tasks in DeepMind Control Suites.
  • Figure 5: Overall performance on MetaWorld tasks.
  • ...and 2 more figures

Theorems & Definitions (15)

  • Definition 1: $L$-decodability efroni2022provable
  • Definition 2: $\gamma$-observability golowich2022learningeven2007value
  • Theorem 3: PAC Guarantee, Informal version of Theorem \ref{['thm:pac_guarantee_online']}
  • Theorem 4: Proprosition 7 guo2023provably, Lemma 12 uehara2022provably
  • Definition 5: Moment Matching Policy efroni2022provable
  • Definition 6: Kernel and Reproducing Kernel Hilbert Space (RKHS) aronszajn1950theorypaulsen2016introduction
  • Theorem 7: Mercer's Theorem riesz2012functionalsteinwart2012mercer
  • Definition 8: Random Feature
  • Lemma 9: $L$-step back inequality for the true model
  • Lemma 10: $L$-step back inequality for the learned model
  • ...and 5 more