[Paper Review] Learning Modular Safe Policies in the Bandit Setting with Application to Adaptive Clinical Trials

Hossein Aboutalebi, Doina Precup+1 more|arXiv (Cornell University)|Mar 4, 2019

Advanced Bandit Algorithms Research11 references3 citations

TL;DR

This paper introduces a modular safety-aware regret framework for multi-armed bandits, enabling flexible definition of risk beyond expected reward. It proposes BESA+, a modified BESA algorithm that achieves low regret under diverse safety criteria, outperforming standard bandit methods in synthetic and real clinical trial datasets, particularly in favoring consistent treatments over high-mean, high-variance alternatives.

ABSTRACT

The stochastic multi-armed bandit problem is a well-known model for studying the exploration-exploitation trade-off. It has significant possible applications in adaptive clinical trials, which allow for dynamic changes in the treatment allocation probabilities of patients. However, most bandit learning algorithms are designed with the goal of minimizing the expected regret. While this approach is useful in many areas, in clinical trials, it can be sensitive to outlier data, especially when the sample size is small. In this paper, we define and study a new robustness criterion for bandit problems. Specifically, we consider optimizing a function of the distribution of returns as a regret measure. This provides practitioners more flexibility to define an appropriate regret measure. The learning algorithm we propose to solve this type of problem is a modification of the BESA algorithm [Baransi et al., 2014], which considers a more general version of regret. We present a regret bound for our approach and evaluate it empirically both on synthetic problems as well as on a dataset from the clinical trial literature. Our approach compares favorably to a suite of standard bandit algorithms.

Motivation & Objective

• To address the limitations of standard bandit algorithms in clinical trials, where only expected reward is optimized and outliers or variance can distort outcomes.
• To develop a modular regret definition that allows practitioners to define safety and consistency based on domain-specific risk preferences.
• To extend the BESA algorithm to handle arbitrary safety-aware regret functions while maintaining low hyper-parameter sensitivity.
• To empirically validate BESA+ on synthetic environments and real clinical trial data, demonstrating superior performance in consistency-focused settings.
• To provide a publicly accessible web simulator for benchmarking bandit algorithms under user-defined safety criteria.

Proposed method

• Proposes a modular safety-aware regret function that generalizes expected regret to include distributional properties such as variance, CVaR, or mean-variance trade-offs.
• Modifies the BESA algorithm (BESA+) to optimize the new safety-aware regret, using empirical mean and McDiarmid's inequality for concentration bounds.
• Employs a sampling-based approach to estimate the safety-aware value function, enabling adaptation to arbitrary risk measures without requiring parametric assumptions.
• Uses a UCB-style exploration strategy with safety-aware confidence bounds derived from empirical risk estimates.
• Applies theoretical regret bounds based on McDiarmid’s Lemma to ensure convergence under mild regularity conditions on the safety function.
• Develops a web-based simulator allowing users to define custom bandit environments and compare algorithm performance in real time.

Experimental results

Research questions

• RQ1 Can a modular regret framework improve robustness in bandit learning when applied to clinical trials with small sample sizes and outlier-sensitive outcomes?
• RQ2 How does BESA+ perform compared to standard bandit algorithms (e.g., UCB1, Thompson Sampling, MV-LCB) under safety-aware regret definitions like CVaR and mean-variance?
• RQ3 Does BESA+ favor more consistent treatments over high-mean, high-variance treatments in real-world clinical data, even when the latter has higher average survival time?
• RQ4 Can the proposed framework support arbitrary safety-aware regret functions without requiring algorithmic re-design?
• RQ5 To what extent does the web-based simulator enable reproducible benchmarking of bandit algorithms under diverse safety criteria?

Key findings

• BESA+ achieved lower accumulated regret than UCB1, Thompson Sampling, MV-LCB, and ExpExp in synthetic two-armed and multi-armed Gaussian mixture bandit environments under both CVaR and mean-variance safety functions.
• In the real clinical trial dataset from lung cancer patients, BESA+ consistently favored treatment 1, which had lower variance and higher consistency, despite treatment 2 having a higher mean survival time.
• The percentage of optimal arm plays under BESA+ was consistently higher than baseline methods, especially in high-variance environments, indicating better exploitation of stable treatments.
• BESA+ demonstrated lower variance across 10 independent experiments under both safety criteria, indicating robustness to random initialization and data fluctuations.
• The web application simulator successfully enabled real-time comparison of bandit algorithms across user-defined environments, supporting reproducibility and extensibility.
• Theoretical analysis shows that BESA+ achieves asymptotic regret bounds under mild assumptions on the safety value function, confirming its admissibility as a learning policy.