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Multi-State TD Target for Model-Free Reinforcement Learning

Wuhao Wang, Zhiyong Chen, Lepeng Zhang

TL;DR

The paper introduces a multi-state TD target (MSTD) that averages multi-step TD targets across multiple future states to improve value estimation in model-free reinforcement learning. It integrates MSTD with actor-critic methods (DDPG and SAC) and proposes two replay-buffer modes—action-loaded and action-generated—to support updates using information from multiple states. Empirical results on continuous-control benchmarks (Walker-v4 and HalfCheetah-v4) show that MSTD-based algorithms outperform traditional multi-step methods, with the two modes offering different advantages depending on the environment. The work provides convergence analysis and extends maximum-entropy ideas to the MSTD framework, offering a practical path to more sample-efficient learning in continuous control.

Abstract

Temporal difference (TD) learning is a fundamental technique in reinforcement learning that updates value estimates for states or state-action pairs using a TD target. This target represents an improved estimate of the true value by incorporating both immediate rewards and the estimated value of subsequent states. Traditionally, TD learning relies on the value of a single subsequent state. We propose an enhanced multi-state TD (MSTD) target that utilizes the estimated values of multiple subsequent states. Building on this new MSTD concept, we develop complete actor-critic algorithms that include management of replay buffers in two modes, and integrate with deep deterministic policy optimization (DDPG) and soft actor-critic (SAC). Experimental results demonstrate that algorithms employing the MSTD target significantly improve learning performance compared to traditional methods.The code is provided on GitHub.

Multi-State TD Target for Model-Free Reinforcement Learning

TL;DR

The paper introduces a multi-state TD target (MSTD) that averages multi-step TD targets across multiple future states to improve value estimation in model-free reinforcement learning. It integrates MSTD with actor-critic methods (DDPG and SAC) and proposes two replay-buffer modes—action-loaded and action-generated—to support updates using information from multiple states. Empirical results on continuous-control benchmarks (Walker-v4 and HalfCheetah-v4) show that MSTD-based algorithms outperform traditional multi-step methods, with the two modes offering different advantages depending on the environment. The work provides convergence analysis and extends maximum-entropy ideas to the MSTD framework, offering a practical path to more sample-efficient learning in continuous control.

Abstract

Temporal difference (TD) learning is a fundamental technique in reinforcement learning that updates value estimates for states or state-action pairs using a TD target. This target represents an improved estimate of the true value by incorporating both immediate rewards and the estimated value of subsequent states. Traditionally, TD learning relies on the value of a single subsequent state. We propose an enhanced multi-state TD (MSTD) target that utilizes the estimated values of multiple subsequent states. Building on this new MSTD concept, we develop complete actor-critic algorithms that include management of replay buffers in two modes, and integrate with deep deterministic policy optimization (DDPG) and soft actor-critic (SAC). Experimental results demonstrate that algorithms employing the MSTD target significantly improve learning performance compared to traditional methods.The code is provided on GitHub.
Paper Structure (11 sections, 3 theorems, 38 equations, 6 figures, 3 tables, 1 algorithm)

This paper contains 11 sections, 3 theorems, 38 equations, 6 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Multi-state Temporal Difference
  5. Algorithms
  6. Maintenance of a Replay Buffer
  7. Action-loaded and Action-generated Modes
  8. Action-loaded DDPG with MSTD
  9. Integration with Maximum Entropy
  10. Experiments
  11. Conclusion

Key Result

Lemma 1

A random process converges to zero w.p.1 under the following assumptions: where $P_t$ stands for the past at step $t$, $a_t$ and $F_t$ are allowed to depend on the past insofar as the above conditions remain valid. The notation $\|\cdot\|_\infty$ indicates the maximum norm and $\left\|\Delta_t\right\|_\infty = \max_{x} |\Delta_t(x)|$.

Figures (6)

  • Figure 1: Management of sample structure in a replay buffer.
  • Figure 2: Two modes of sample structure in a replay buffer.
  • Figure 3: Performance comparison of various DDPG algorithms in Walker-v4 environment.
  • Figure 4: Performance comparison of various SAC algorithms in Walker-v4 environment.
  • Figure 5: Performance comparison of various DDPG algorithms in HalfCheetah-v4 environment.
  • ...and 1 more figures

Theorems & Definitions (5)

  • Lemma 1
  • Lemma 2
  • proof
  • Theorem 1
  • proof