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 $T\to\infty$. 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.

Public models offer predictions to a variety of downstream tasks and have played a crucial role in various AI applications, showcasing their proficiency in accurate predictions. However, the exclusive emphasis on prediction accuracy may not align with the diverse end objectives of downstream agents. Recognizing the public model's predictions as a service, we advocate for integrating the objectives of downstream agents into the optimization process. Concretely, to address performance disparities and foster fairness among heterogeneous agents in training, we propose a novel Equitable Objective. This objective, coupled with a policy gradient algorithm, is crafted to train the public model to produce a more equitable/uniform performance distribution across downstream agents, each with their unique concerns. Both theoretical analysis and empirical case studies have proven the effectiveness of our method in advancing performance equity across diverse downstream agents utilizing the public model for their decision-making. Codes and datasets are released at https://github.com/Ren-Research/Socially-Equitable-Public-Models.

Online Budgeted Matching (OBM) is a classic problem with important applications in online advertising, online service matching, revenue management, and beyond. Traditional online algorithms typically assume a small bid setting, where the maximum bid-to-budget ratio ($\kappa$) is infinitesimally small. While recent algorithms have tried to address scenarios with non-small or general bids, they often rely on the Fractional Last Matching (FLM) assumption, which allows for accepting partial bids when the remaining budget is insufficient. This assumption, however, does not hold for many applications with indivisible bids. In this paper, we remove the FLM assumption and tackle the open problem of OBM with general bids. We first establish an upper bound of $1-\kappa$ on the competitive ratio for any deterministic online algorithm. We then propose a novel meta algorithm, called MetaAd, which reduces to different algorithms with first known provable competitive ratios parameterized by the maximum bid-to-budget ratio $\kappa\in [0,1]$. As a by-product, we extend MetaAd to the FLM setting and get provable competitive algorithms. Finally, we apply our competitive analysis to the design learning- augmented algorithms.

Many problems, such as online ad display, can be formulated as online bipartite matching. The crucial challenge lies in the nature of sequentially-revealed online item information, based on which we make irreversible matching decisions at each step. While numerous expert online algorithms have been proposed with bounded worst-case competitive ratios, they may not offer satisfactory performance in average cases. On the other hand, reinforcement learning (RL) has been applied to improve the average performance, but it lacks robustness and can perform arbitrarily poorly. In this paper, we propose a novel RL-based approach to edge-weighted online bipartite matching with robustness guarantees (LOMAR), achieving both good average-case and worst-case performance. The key novelty of LOMAR is a new online switching operation which, based on a judicious condition to hedge against future uncertainties, decides whether to follow the expert’s decision or the RL decision for each online item. We prove that for any $\rho\in[0,1]$, LOMAR is $\rho$-competitive against any given expert online algorithm. To improve the average performance, we train the RL policy by explicitly considering the online switching operation. Finally, we run empirical experiments to demonstrate the advantages of LOMAR compared to existing baselines.

Online optimization with memory costs has many real-world applications, where sequential actions are made without knowing the future input. Nonetheless, the memory cost couples the actions over time, adding substantial challenges. Conventionally, this problem has been approached by various expert-designed online algorithms with the goal of achieving bounded worst-case competitive ratios, but the resulting average performance is often unsatisfactory. On the other hand, emerging machine learning (ML) based optimizers can improve the average performance, but suffer from the lack of worst-case performance robustness. In this paper, we propose a novel expert-robustified learning (ERL) approach, achieving both good average performance and robustness. More concretely, for robustness, ERL introduces a novel projection operator that robustifies ML actions by utilizing an expert online algorithm; for average performance, ERL trains the ML optimizer based on a recurrent architecture by explicitly considering downstream expert robustification. We prove that, for any λ ≥ 1, ERL can achieve λ-competitive against the expert algorithm and λ•C-competitive against the optimal offline algorithm (where C is the expert’s competitive ratio). Additionally, we extend our analysis to a novel setting of multi-step memory costs. Finally, our analysis is supported by empirical experiments for an energy scheduling application.

We study a general form of Smoothed Online Convex Optimization, a.k.a. SOCO, including multi-step switching costs and feedback delay. We propose a novel machine learning (ML) augmented online algorithm, Robustness-Constrained Learning (RCL), which combines untrusted ML predictions with a trusted expert online algorithm via constrained projection to robustify the ML prediction. Specifically, we prove that RCL is able to guarantee $(1+\lambda)$-competitiveness against any given expert for any $\lambda>0$, while also explicitly training the ML model in a robustification-aware manner to improve the average-case performance. Importantly, RCL is the first ML-augmented algorithm with a provable robustness guarantee in the case of multi-step switching cost and feedback delay. We demonstrate the improvement of RCL in both robustness and average performance using battery management as a case study.

This paper studies the problem of Anytime-Competitive Markov Decision Process (A-CMDP). Existing works on Constrained Markov Decision Processes (CMDPs) aim to optimize the expected reward while constraining the expected cost over random dynamics, but the cost in a specific episode can still be unsatisfactorily high. In contrast, the goal of A-CMDP is to optimize the expected reward while guaranteeing a bounded cost in each round of any episode against a policy prior. We propose a new algorithm, called Anytime-Competitive Reinforcement Learning (ACRL), which provably guarantees the anytime cost constraints. The regret analysis shows the policy asymptotically matches the optimal reward achievable under the anytime competitive constraints. Experiments on the application of carbon-intelligent computing verify the reward performance and cost constraint guarantee of ACRL.