Jianyi Yang

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 (κ) 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 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 . 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.

This paper studies online resource allocation with replenishable budgets, where budgets can be replenished on top of the initial budget and an agent sequentially chooses online allocation decisions without violating the available budget constraint at each round. We propose a novel online algorithm, called OACP (Opportunistic Allocation with Conservative Pricing), that conservatively adjusts dual variables while opportunistically utilizing available resources. OACP achieves a bounded asymptotic competitive ratio in adversarial settings as the number of decision rounds T gets large. Importantly, the asymptotic competitive ratio of OACP is optimal in the absence of additional assumptions on budget replenishment. To further improve the competitive ratio, we make a mild assumption that there is budget replenishment every T* decision rounds and propose OACP+ to dynamically adjust the total budget assignment for online allocation. Next, we move beyond the worst-case and propose LA-OACP (Learning-Augmented OACP/OACP+), a novel learning-augmented algorithm for online allocation with replenishable budgets. We prove that LA-OACP can improve the average utility compared to OACP/OACP+ when the ML predictor is properly trained, while still offering worst-case utility guarantees when the ML predictions are arbitrarily wrong. Finally, we run simulation studies of sustainable AI inference powered by renewables, validating our analysis and demonstrating the empirical benefits of LA-OACP.

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.

By integrating domain knowledge with labeled samples, informed machine learning has been emerging to improve the learning performance for a wide range of applications. Nonetheless, rigorous understanding of the role of injected domain knowledge has been under-explored. In this paper, we consider an informed deep neural network (DNN) with over-parameterization and domain knowledge integrated into its training objective function, and study how and why domain knowledge benefits the performance. Concretely, we quantitatively demonstrate the two benefits of domain knowledge in informed learning — regularizing the label-based supervision and supplementing the labeled samples — and reveal the trade-off between label and knowledge imperfectness in the bound of the population risk. Based on the theoretical analysis, we propose a generalized informed training objective to better exploit the benefits of knowledge and balance the label and knowledge imperfectness, which is validated by the population risk bound. Our analysis on sampling complexity sheds lights on how to choose the hyper-parameters for informed learning, and further justifies the advantages of knowledge informed learning.

We study online convex optimization with switching costs, a practically important but also extremely chal- lenging problem due to the lack of complete offline information. By tapping into the power of machine learning (ML) based optimizers, ML-augmented online algorithms (also referred to as expert calibration in this paper) have been emerging as state of the art, with provable worst-case performance guarantees. Nonetheless, by using the standard practice of training an ML model as a standalone optimizer and plugging it into an ML-augmented algorithm, the average cost performance can be highly unsatisfactory. In order to address the “how to learn” challenge, we propose EC-L2O (expert-calibrated learning to optimize), which trains an ML-based optimizer by explicitly taking into account the downstream expert calibrator. To accomplish this, we propose a new differentiable expert calibrator that generalizes regularized online balanced descent and offers a provably better competitive ratio than pure ML predictions when the prediction error is large. For training, our loss function is a weighted sum of two different losses — one minimizing the average ML prediction error for better robustness, and the other one minimizing the post-calibration average cost. We also provide theoretical analysis for EC-L2O, highlighting that expert calibration can be even beneficial for the average cost performance and that the high-percentile tail ratio of the cost achieved by EC-L2O to that of the offline optimal oracle (i.e., tail cost ratio) can be bounded. Finally, we test EC-L2O by running simulations for sustainable datacenter demand response. Our results demonstrate that EC-L2O can empirically achieve a lower average cost as well as a lower competitive ratio than the existing baseline algorithms.