Provably Efficient Reinforcement Learning for Adversarial Restless Multi-Armed Bandits with Unknown Transitions and Bandit Feedback

Core Concepts

The authors develop a novel reinforcement learning algorithm, UCMD-ARMAB, that achieves a regret bound of ˜O(H√T) for adversarial restless multi-armed bandits with unknown transitions and bandit feedback, where T is the number of episodes and H is the episode length.

Abstract

The content presents a reinforcement learning algorithm, UCMD-ARMAB, for solving the problem of learning in episodic adversarial restless multi-armed bandits (ARMAB) with unknown transition functions and bandit feedback.
Key highlights:

ARMAB models sequential decision making problems under an instantaneous activation constraint, where at most B arms can be activated at any decision epoch. Each arm evolves stochastically according to a Markov decision process.
The authors consider a challenging setting where the adversarial rewards can change arbitrarily between episodes, and only the rewards of visited state-action pairs are revealed (bandit feedback).
UCMD-ARMAB has four main components:

Maintaining confidence sets for the unknown transition functions.
Using online mirror descent to solve a relaxed version of ARMAB in terms of occupancy measures to handle adversarial rewards.
Constructing a novel biased adversarial reward estimator to deal with bandit feedback.
Designing a low-complexity index policy to satisfy the instantaneous activation constraint.

The authors prove that UCMD-ARMAB achieves a regret bound of ˜O(H√T), which is the first ˜O(√T) regret result for adversarial RMAB with unknown transitions and bandit feedback.

Stats

The number of episodes T is the total time horizon.
The length of each episode is H.
The number of arms is N.
The instantaneous activation constraint allows at most B arms to be activated at any decision epoch.

Quotes

"To our best knowledge, this is the first algorithm to ensure ˜O(√T) regret for adversarial RMAB in our considered challenging settings."
"Although our regret bound exhibits a gap (i.e., √H times larger) to that of stochastic RMAB (Xiong et al., 2022a;c), to our best knowledge, our result is the first to achieve ˜O(√T) regret."

Key Insights Distilled From

Provably Efficient Reinforcement Learning for Adversarial Restless Multi-Armed Bandits with Unknown Transitions and Bandit Feedback

by Guojun Xiong... at arxiv.org 05-03-2024

https://arxiv.org/pdf/2405.00950.pdf

Deeper Inquiries

How can the proposed UCMD-ARMAB algorithm be extended to handle partial observability or function approximation in the transition dynamics and reward functions

To extend the UCMD-ARMAB algorithm to handle partial observability, one approach could be to incorporate techniques from partially observable Markov decision processes (POMDPs). By introducing belief states that capture the uncertainty about the true state of the system, the algorithm can make decisions based on the current belief state rather than the observed state. This would involve updating the belief state using the observed actions and rewards, and incorporating it into the decision-making process.
For function approximation in the transition dynamics and reward functions, the UCMD-ARMAB algorithm can leverage techniques from approximate dynamic programming. By using function approximators such as neural networks or linear models, the algorithm can learn an approximation of the transition dynamics and reward functions. This would involve updating the function approximators based on the observed data and using them to make predictions about the next state and expected rewards.

What are the potential applications of adversarial RMAB beyond the examples mentioned in the content, and how can the UCMD-ARMAB algorithm be adapted to those domains

The UCMD-ARMAB algorithm can be adapted to various domains beyond the examples mentioned in the content. Some potential applications of adversarial RMAB include cybersecurity, finance, and autonomous systems. In cybersecurity, the algorithm could be used to optimize security measures against adversarial attacks. In finance, it could help in portfolio optimization under changing market conditions. For autonomous systems, it could be applied to decision-making in dynamic environments.
To adapt the UCMD-ARMAB algorithm to these domains, specific domain knowledge would need to be incorporated into the algorithm. This could involve customizing the reward functions, transition dynamics, and constraints to align with the specific requirements of the domain. Additionally, the algorithm may need to be modified to handle the unique challenges and characteristics of each application area.

Can the techniques developed in this work be applied to other constrained reinforcement learning problems beyond RMAB to achieve improved regret bounds

The techniques developed in this work can be applied to other constrained reinforcement learning problems beyond RMAB to achieve improved regret bounds. For example, in constrained Markov decision processes (CMDPs), where policies need to satisfy certain constraints while maximizing rewards, the UCMD-ARMAB algorithm's approach to handling constraints and optimizing rewards could be beneficial.
By adapting the algorithm to CMDPs, the regret bounds could be further improved by incorporating the specific constraints of CMDPs into the decision-making process. This could involve developing specialized policies that balance the trade-off between maximizing rewards and satisfying constraints. Additionally, the techniques for handling unknown transitions and bandit feedback could be extended to CMDPs to address the challenges of learning in such environments.