Near-Optimal Reinforcement Learning Algorithm for Zero-Delay Coding of Markov Sources

Core Concepts

A reinforcement learning algorithm is presented that can efficiently compute near-optimal zero-delay coding policies for Markov sources, overcoming the computational challenges of previous approaches.

Abstract

The paper considers the problem of encoding and decoding a finite-alphabet Markov source without any delay, known as the zero-delay lossy coding problem. This problem can be formulated as a Markov Decision Process (MDP) with the belief state (conditional probability distribution of the current source symbol) as the state and the quantizer as the action.

The key insights are:

1. The MDP formulation has an uncountable state space (the set of beliefs), making traditional dynamic programming and value iteration methods computationally prohibitive.

2. The authors present a quantized Q-learning algorithm that can efficiently compute a near-optimal coding policy by discretizing the belief state space.

3. The authors prove the asymptotic optimality of the proposed algorithm, first for the discounted cost problem and then for the average cost problem, by relating the optimal solutions for the two criteria.

4. The technical analysis involves showing the unique ergodicity of the belief process under a memoryless exploration policy, which is necessary for the convergence of the Q-learning algorithm.

5. Simulations demonstrate the superior performance of the proposed algorithm compared to existing heuristic techniques for zero-delay coding.

Stats

The source {Xt}t≥0 is a time-homogeneous, discrete-time Markov process taking values in a finite set X and has transition matrix P(xt+1|xt).
The encoded information qt is sent over a discrete noiseless channel with common input and output alphabet M := {1, . . . , M}.
The goal is to minimize the average distortion J(π0, γ) := lim supT→∞ Eγ
π0 [1/T ∑T−1
t=0 d(Xt, X̂t)], where d : X × X̂ → [0, ∞) is a given distortion measure.

Quotes

"The MDP formulation has an uncountable state space (the set of beliefs), making traditional dynamic programming and value iteration methods computationally prohibitive."
"The authors present a quantized Q-learning algorithm that can efficiently compute a near-optimal coding policy by discretizing the belief state space."
"The authors prove the asymptotic optimality of the proposed algorithm, first for the discounted cost problem and then for the average cost problem, by relating the optimal solutions for the two criteria."

Key Insights Distilled From

Reinforcement Learning for Near-Optimal Design of Zero-Delay Codes for Markov Sources

by Liam Cregg,T... at arxiv.org 05-07-2024

https://arxiv.org/pdf/2311.12609.pdf

Deeper Inquiries

How can the proposed reinforcement learning algorithm be extended to handle continuous-alphabet Markov sources

To extend the proposed reinforcement learning algorithm to handle continuous-alphabet Markov sources, we need to address the challenges posed by the uncountable state space. One approach could involve discretizing the continuous state space into a finite number of bins, similar to the quantization process used for the finite-alphabet Markov sources. By discretizing the state space, we can apply the quantized Q-learning algorithm to approximate the optimal policy for the continuous-alphabet Markov sources. Additionally, techniques such as function approximation or deep reinforcement learning can be employed to handle the continuous state space more efficiently. These methods involve approximating the value function or policy using neural networks, allowing for a more scalable and accurate representation of the state space.

What are the implications of the unique ergodicity result for the belief process under the memoryless exploration policy, and how can it be leveraged in other applications

The unique ergodicity result for the belief process under the memoryless exploration policy has significant implications for the stability and convergence properties of the system. It ensures that the belief process converges to a unique invariant measure, indicating that the system reaches a steady state under the exploration policy. This result can be leveraged in various applications, such as in reinforcement learning, where stability and convergence are crucial for the learning process. By understanding the behavior of the belief process under the memoryless exploration policy, we can design more robust and efficient algorithms for stochastic control problems. Additionally, the unique ergodicity result provides insights into the long-term behavior of the system, aiding in the analysis and optimization of complex systems with measure-valued state spaces.

Can the techniques developed in this work be applied to other stochastic control problems with measure-valued state spaces

The techniques developed in this work, such as quantized Q-learning and the analysis of unique ergodicity, can be applied to other stochastic control problems with measure-valued state spaces. By adapting the reinforcement learning algorithm and the stability analysis to different problem settings, we can address a wide range of applications in control theory, optimization, and decision-making. These techniques can be particularly useful in problems involving complex systems with uncertain dynamics and continuous state spaces. By leveraging the principles of reinforcement learning and stochastic control, we can develop efficient and adaptive solutions for a variety of real-world problems, ranging from autonomous systems to financial modeling and beyond.