Adversarial Bandit Optimization with Globally Bounded Perturbations to Convex Losses

2026-06-18 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Expert, quick

Summary

A new study introduces a framework for adversarial bandit optimization, specifically addressing scenarios where loss functions are non-convex and non-smooth. In this model, a learner selects an action and observes only the incurred loss, which comprises an underlying convex and β-smooth component, plus an adversarial perturbation. Crucially, these perturbations can be chosen after the learner's action and are constrained by a global budget on their cumulative magnitude over time. This work extends previous models that focused solely on linear losses to encompass general convex and β-smooth losses. The authors establish expected regret guarantees that precisely quantify the impact of the perturbation budget, achieved by modifying a standard bandit optimization algorithm and developing a specialized analysis to control additional regret. In the absence of perturbations, these results align with standard bandit convex optimization guarantees for β-smooth losses.

Key takeaway

For Research Scientists developing online learning algorithms, this work offers critical insights into managing adversarial perturbations. It extends regret guarantees for bandit optimization to general convex and β-smooth losses, even with post-action, globally budgeted adversarial noise. You should consider how the proposed algorithm modification and analysis of perturbation effects can inform the design of more robust online learning systems, particularly in settings with unpredictable adversaries.

Key insights

This work extends adversarial bandit optimization to general convex and β-smooth losses with globally bounded post-action perturbations.

Principles

• Adversarial perturbations can be globally budgeted.
• Post-action perturbations impact regret guarantees.
• Standard algorithms adapt to handle perturbations.

Method

Modify a standard bandit optimization algorithm and develop an analysis to control additional regret caused by globally bounded adversarial perturbations.

In practice

• Design robust online learning systems.
• Analyze performance under adversarial noise.
• Benchmark bandit algorithms.

Topics

• Adversarial Bandit Optimization
• Convex Optimization
• Regret Guarantees
• Online Learning
• Machine Learning
• Perturbation Theory

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.