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Fast Value Tracking for Deep Reinforcement Learning

Frank Shih, Faming Liang

TL;DR

The paper tackles the lack of uncertainty quantification and dynamic tracking in deep reinforcement learning by introducing LKTD, a Langevinized Kalman Temporal-Difference method. LKTD casts RL as a nonlinear state-space model with a prior over parameters and uses Langevinized Ensemble Kalman filtering to draw posterior samples of deep network weights, enabling both value estimation and uncertainty quantification. The authors prove convergence to a stationary posterior distribution under mild conditions, and demonstrate scalability with $O(np)$ per-iteration complexity, including replay-buffer support for off-policy learning. Empirically, LKTD improves Q-value accuracy, provides well-calibrated prediction intervals, and enhances policy exploration across indoor and classical control tasks, outperforming several strong baselines. This approach offers a principled, uncertainty-aware, and data-efficient path for robust deep RL.

Abstract

Reinforcement learning (RL) tackles sequential decision-making problems by creating agents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model parameters to maximize expected rewards, neglecting the stochastic dynamics of agent-environment interactions and the critical role of uncertainty quantification. Our research leverages the Kalman filtering paradigm to introduce a novel and scalable sampling algorithm called Langevinized Kalman Temporal-Difference (LKTD) for deep reinforcement learning. This algorithm, grounded in Stochastic Gradient Markov Chain Monte Carlo (SGMCMC), efficiently draws samples from the posterior distribution of deep neural network parameters. Under mild conditions, we prove that the posterior samples generated by the LKTD algorithm converge to a stationary distribution. This convergence not only enables us to quantify uncertainties associated with the value function and model parameters but also allows us to monitor these uncertainties during policy updates throughout the training phase. The LKTD algorithm paves the way for more robust and adaptable reinforcement learning approaches.

Fast Value Tracking for Deep Reinforcement Learning

TL;DR

The paper tackles the lack of uncertainty quantification and dynamic tracking in deep reinforcement learning by introducing LKTD, a Langevinized Kalman Temporal-Difference method. LKTD casts RL as a nonlinear state-space model with a prior over parameters and uses Langevinized Ensemble Kalman filtering to draw posterior samples of deep network weights, enabling both value estimation and uncertainty quantification. The authors prove convergence to a stationary posterior distribution under mild conditions, and demonstrate scalability with per-iteration complexity, including replay-buffer support for off-policy learning. Empirically, LKTD improves Q-value accuracy, provides well-calibrated prediction intervals, and enhances policy exploration across indoor and classical control tasks, outperforming several strong baselines. This approach offers a principled, uncertainty-aware, and data-efficient path for robust deep RL.

Abstract

Reinforcement learning (RL) tackles sequential decision-making problems by creating agents that interacts with their environment. However, existing algorithms often view these problem as static, focusing on point estimates for model parameters to maximize expected rewards, neglecting the stochastic dynamics of agent-environment interactions and the critical role of uncertainty quantification. Our research leverages the Kalman filtering paradigm to introduce a novel and scalable sampling algorithm called Langevinized Kalman Temporal-Difference (LKTD) for deep reinforcement learning. This algorithm, grounded in Stochastic Gradient Markov Chain Monte Carlo (SGMCMC), efficiently draws samples from the posterior distribution of deep neural network parameters. Under mild conditions, we prove that the posterior samples generated by the LKTD algorithm converge to a stationary distribution. This convergence not only enables us to quantify uncertainties associated with the value function and model parameters but also allows us to monitor these uncertainties during policy updates throughout the training phase. The LKTD algorithm paves the way for more robust and adaptable reinforcement learning approaches.
Paper Structure (26 sections, 4 theorems, 65 equations, 9 figures, 5 tables, 5 algorithms)

This paper contains 26 sections, 4 theorems, 65 equations, 9 figures, 5 tables, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Works
  3. Background
  4. Markov Decision Process
  5. Kalman Temporal Difference (KTD) Algorithms
  6. Langevinized Kalman Temporal Difference Algorithm
  7. The LKTD Algorithm
  8. Convergence Theory
  9. Convergence of the LKTD algorithm under the on-policy setting
  10. Cooperation with Replay Buffer
  11. Experiments
  12. Indoor escape environment
  13. Classical control problems
  14. Conclusion
  15. Appendix
  16. ...and 11 more sections

Key Result

Lemma 1

Algorithm alg:prototype implements a preconditioned SGLD algorithm, for which where ${\bm{z}}_{t} = ({\bm{r}}_t, {\bm{x}}_t)$ as defined in Algorithm alg:prototype, $\Sigma_t = \frac{n}{\mathcal{N}}(I-K_t H_t)$ is a constant matrix given $\varphi_t$, $e_t\sim N(0, \epsilon_t \Sigma_t)$, and the gradient term $\nabla_{\varphi} \log \pi(\varphi_{t-1}^a|{\bm{z}}_{t})$ is given b

Figures (9)

  • Figure 1: Indoor escape environment
  • Figure 2: Boxplots for MSE($\hat{Q}_a$) (for $a\in \{N,E\})$)
  • Figure 3: Boxplots for coverage rates (for $a\in \{N,E\})$)
  • Figure 4: Mean policy probabilities for the indoor escape environment: (a) known optimal solution; (b) learned by LKTD; (c) learned by DQN, failing to explore different policies.
  • Figure 5: CartPole-v1: The left plot shows the cumulative rewards obtained during the training process, the middle plot shows the testing performance without random exploration, and the right plot shows the performance of best model learned up to the point $t$.
  • ...and 4 more figures

Theorems & Definitions (9)

  • Lemma 1
  • Theorem 1
  • Remark 1
  • Remark 2
  • Corollary 1
  • Theorem 2
  • proof
  • proof
  • proof