Reinforcement Learning with Bottleneck and Other Non-Cumulative Objectives

Core Concepts

This paper proposes a modification to existing reinforcement learning algorithms to optimize non-cumulative objectives, such as the bottleneck reward, maximum reward, and harmonic mean reward, which are prevalent in various application domains like communications and networking.

Abstract

The paper recognizes that many optimal control and reinforcement learning problems have objectives that are not naturally expressed as summations of rewards, and proposes a generalization of the Bellman optimality equation to handle such non-cumulative objectives.

The key highlights are:

1. The authors identify the prevalence of non-cumulative objectives in various application domains, especially in communications and networking problems.

2. They propose a modification to the Bellman update rule, replacing the summation operation with a generalized operation corresponding to the objective function.

3. Theoretical analysis is provided, establishing sufficient conditions on the form of the generalized operation and assumptions on the Markov decision process, under which the globally optimal convergence of the generalized Bellman updates can be guaranteed.

4. The authors demonstrate the effectiveness of the proposed approach on classical optimal control and reinforcement learning tasks, as well as on network routing problems, where the bottleneck objective is particularly relevant.

5. Experimental results show that the proposed generalized Bellman updates can achieve competitive or better performance compared to the conventional approaches, while being more efficient and stable, especially in the multi-agent reinforcement learning setting.

Stats

The paper does not provide any specific numerical data or statistics to support the key claims. The focus is on the theoretical analysis and the experimental demonstrations of the proposed approach.

Quotes

"In reinforcement learning, the objective is almost always defined as a cumulative function over the rewards along the process. However, there are many optimal control and reinforcement learning problems in various application fields, especially in communications and networking, where the objectives are not naturally expressed as summations of the rewards."
"To optimize a non-cumulative objective, we replace the original summation operation in the Bellman update rule with a generalized operation corresponding to the objective."

Key Insights Distilled From

Reinforcement Learning with Non-Cumulative Objective

by Wei Cui,Wei ... at arxiv.org 04-15-2024

https://arxiv.org/pdf/2307.04957.pdf

Deeper Inquiries

What other types of non-cumulative objectives, beyond the examples provided, could be optimized using the proposed generalized Bellman update approach

In addition to the examples provided in the context, there are several other types of non-cumulative objectives that could be optimized using the proposed generalized Bellman update approach. One such objective could be the "maximum-minimum" objective, where the agent aims to maximize the minimum value among a set of intermediate rewards. This objective could be applicable in scenarios where the agent needs to ensure a certain level of performance across multiple criteria, with the goal of optimizing the worst-case scenario. Another type of non-cumulative objective could be the "penalized sum" objective, where the agent aims to minimize the sum of rewards while penalizing specific negative outcomes. This objective could be useful in situations where certain actions have high costs or risks associated with them, and the agent needs to balance between achieving rewards and avoiding penalties.

How would the proposed method perform in more complex, large-scale multi-agent reinforcement learning scenarios, such as in highly dynamic and uncertain environments

In more complex, large-scale multi-agent reinforcement learning scenarios, such as those in highly dynamic and uncertain environments, the proposed generalized Bellman update approach could still be effective. The flexibility of the approach in handling non-cumulative objectives allows for a wide range of optimization possibilities, even in complex environments. By adapting the Bellman update rule to accommodate different types of objectives, the agents can learn to make decisions that are aligned with the overall goals of the system. However, in highly dynamic and uncertain environments, the convergence and stability of the learning process may require additional considerations. Techniques such as prioritized experience replay, adaptive exploration strategies, and ensemble learning could be employed to enhance the performance and robustness of the agents in such scenarios.

Can the generalized Bellman update approach be extended to handle partially observable Markov decision processes, where the state information available to the agents is limited

The generalized Bellman update approach can be extended to handle partially observable Markov decision processes (POMDPs), where the state information available to the agents is limited. In POMDPs, the agents do not have full observability of the environment, making it challenging to accurately estimate the value function and make optimal decisions. By incorporating the generalized Bellman update approach, the agents can learn to optimize non-cumulative objectives even in partially observable environments. Techniques such as recurrent neural networks, attention mechanisms, and memory-augmented networks can be utilized to capture the temporal dependencies and partial observability in the state information. Additionally, advanced exploration-exploitation strategies, such as intrinsic motivation and curiosity-driven learning, can help the agents gather relevant information and improve their decision-making in POMDPs.