Fairness-Regularized Online Optimization with Switching Costs

2025-12-11

AI Summary

This paper studies online convex optimization (OCO) with joint objectives of long-term fairness and action smoothness (i.e., switching costs). To address the failure of standard regret analysis under long-term fairness regularization, we introduce, for the first time, an explicit long-term fairness regularizer. We propose FairOBD, an algorithm that online-ifies the non-decomposable long-term fairness cost via auxiliary variable sequences, integrates an extended Online Balanced Descent (OBD) framework, and employs a parameter-constrained offline optimal benchmark. Our novel competitive ratio analysis establishes asymptotic optimality: the competitive ratio converges to a tight lower bound as $T o infty$. Experiments on AI inference resource scheduling demonstrate that FairOBD significantly reduces total fairness cost and more effectively ensures cross-group service fairness compared to baselines.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Philosophy and Ethics of AI: Bias, Fairness & Equity

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Fairness and action smoothness are two crucial considerations in many online optimization problems, but they have yet to be addressed simultaneously. In this paper, we study a new and challenging setting of fairness-regularized smoothed online convex optimization with switching costs. First, to highlight the fundamental challenges introduced by the long-term fairness regularizer evaluated based on the entire sequence of actions, we prove that even without switching costs, no online algorithms can possibly achieve a sublinear regret or finite competitive ratio compared to the offline optimal algorithm as the problem episode length $T$ increases. Then, we propose FairOBD (Fairness-regularized Online Balanced Descent), which reconciles the tension between minimizing the hitting cost, switching cost, and fairness cost. Concretely, FairOBD decomposes the long-term fairness cost into a sequence of online costs by introducing an auxiliary variable and then leverages the auxiliary variable to regularize the online actions for fair outcomes. Based on a new approach to account for switching costs, we prove that FairOBD offers a worst-case asymptotic competitive ratio against a novel benchmark -- the optimal offline algorithm with parameterized constraints -- by considering $T oinfty$. Finally, we run trace-driven experiments of dynamic computing resource provisioning for socially responsible AI inference to empirically evaluate FairOBD, showing that FairOBD can effectively reduce the total fairness-regularized cost and better promote fair outcomes compared to existing baseline solutions.

Problem

• Addresses fairness and smoothness in online optimization with switching costs.
• Proposes FairOBD to balance hitting, switching, and fairness costs.
• Evaluates FairOBD for fair resource provisioning in AI inference.

Innovation

• Fairness-regularized Online Balanced Descent algorithm
• Decomposes long-term fairness into online costs
• Competitive ratio against constrained offline optimal