Efficiency of Slowly Changing Adversarial Bandit Algorithms for Discounted MDPs

Core Concepts

The author explores the efficiency of slowly changing adversarial bandit algorithms in discounted Markov Decision Processes, showing that optimal regret can be achieved. The approach involves a reduction from tabular reinforcement learning to multi-armed bandits.

Abstract

The content discusses the application of slowly changing adversarial bandit algorithms in discounted Markov Decision Processes (MDPs). It explores a reduction from reinforcement learning to bandits, addressing challenges such as objective mismatch and sticky bandits. The analysis includes related works, assumptions, and a case study on EXP3 algorithm. The work highlights the importance of assumptions for exploration in MDPs and suggests potential improvements to reduce dependencies on parameters like state space size and effective horizon. Future directions include exploring stochastic bandit algorithms and extending the framework to function approximation implementations.

Stats

Regret(T) = ˜O(τ 2H4S(S+A)(1−γ)2β3√T) Rfs-mdp(T) = ˜O(H2.5Sf(A)(1−γ)β√T + τ 2H4S(S+A)(1−γ)β3cTT)

Quotes

"We explore a black-box reduction from discounted infinite-horizon tabular reinforcement learning to multi-armed bandits." "Any slowly changing adversarial bandit algorithm achieving optimal regret in the adversarial setting can also attain optimal expected regret in infinite-horizon discounted MDPs." "Our main result requires that the bandits placed in each state are slowly changing."

Key Insights Distilled From

Slowly Changing Adversarial Bandit Algorithms are Efficient for Discounted MDPs

by Ian A. Kash,... at arxiv.org 03-12-2024

https://arxiv.org/pdf/2205.09056.pdf

Deeper Inquiries

How can aggressive local exploration or algorithm-dependent incentives mitigate the need for additional assumptions?

Aggressive local exploration or algorithm-dependent incentives can help mitigate the need for additional assumptions by promoting more thorough exploration of the state space. By encouraging the bandit learners to explore different actions within each state more extensively, these strategies can ensure that all states are visited sufficiently often, reducing the reliance on assumptions about state visitation frequencies. Aggressive local exploration involves prioritizing actions that have not been explored as frequently, allowing for a more comprehensive understanding of the environment and potentially uncovering optimal strategies in underexplored regions. Algorithm-dependent incentives can provide rewards or bonuses based on specific criteria set by the algorithm, encouraging behaviors that align with its learning objectives. By implementing these strategies effectively, bandit algorithms can adapt their decision-making processes to focus on areas where there is uncertainty or lack of information, leading to better overall performance without needing as many external assumptions about state visitation patterns.

How could stochastic bandit algorithms with predefined policy-change times address non-stationary feedback more effectively?

Stochastic bandit algorithms with predefined policy-change times could address non-stationary feedback more effectively by incorporating scheduled updates into their learning process. By defining specific points in time when policies should be adjusted or changed, these algorithms can proactively adapt to shifts in feedback dynamics and optimize their decision-making accordingly. These predefined policy changes allow stochastic bandits to anticipate variations in feedback distribution and adjust their strategies preemptively. This proactive approach enables them to respond quickly to changing conditions without waiting for significant deviations from expected outcomes. Additionally, by introducing controlled policy changes at predetermined intervals, stochastic bandits can maintain a balance between exploration and exploitation while ensuring robustness against non-stationary feedback patterns. This structured approach helps stabilize learning trajectories and improve adaptation capabilities in dynamic environments.