Energy-Efficient Scheduling with Predictions

An important goal of modern scheduling systems is to efficiently manage power usage. In energy-efficient scheduling, the operating system controls the speed at which a machine is processing jobs with the dual objective of minimizing energy consumption and optimizing the quality of service cost of the resulting schedule. Since machine-learned predictions about future requests can often be learned from historical data, a recent line of work on learning-augmented algorithms aims to achieve improved performance guarantees by leveraging predictions. In particular, for energy-efficient scheduling, Bamas et. al. [BamasMRS20] and Antoniadis et. al. [antoniadis2021novel] designed algorithms with predictions for the energy minimization with deadlines problem and achieved an improved competitive ratio when the prediction error is small while also maintaining worst-case bounds even when the prediction error is arbitrarily large. In this paper, we consider a general setting for energy-efficient scheduling and provide a flexible learning-augmented algorithmic framework that takes as input an offline and an online algorithm for the desired energy-efficient scheduling problem. We show that, when the prediction error is small, this framework gives improved competitive ratios for many different energy-efficient scheduling problems, including energy minimization with deadlines, while also maintaining a bounded competitive ratio regardless of the prediction error. Finally, we empirically demonstrate that this framework achieves an improved performance on real and synthetic datasets.

Dynamic pricing and assortment under a contextual MNL demand

We consider dynamic multi-product pricing and assortment problems under an unknown demand over T periods, where in each period, the seller decides on the price for each product or the assortment of products to offer to a customer who chooses according to an unknown Multinomial Logit Model (MNL). Such problems arise in many applications, including online retail and advertising. We propose a randomized dynamic pricing policy based on a variant of the Online Newton Step algorithm (ONS) that achieves a $O(d\sqrt{T}\log(T))$ regret guarantee under an adversarial arrival model. We also present a new optimistic algorithm for the adversarial MNL contextual bandits problem, which achieves a better dependency than the state-of-the-art algorithms in a problem-dependent constant $\kappa$ (potentially exponentially small). Our regret upper bounds scale as $\tilde{O}(d\sqrt{\kappa T}+ \log(T)/\kappa)$, which gives a significantly stronger bound than the existing $\tilde{O}(d\sqrt{T}/\kappa)$ guarantees.

MNL-Bandit with Knapsacks

We consider a dynamic assortment selection problem where a seller has a fixed inventory of $N$ substitutable products and faces an unknown demand that arrives sequentially over $T$ periods. In each period, the seller needs to decide on the assortment of products (of cardinality at most $K$) to offer to the customers. The customer's response follows an unknown multinomial logit model (MNL) with parameters $v$. The goal of the seller is to maximize the total expected revenue given the fixed initial inventory of $N$ products. We give a policy that achieves a regret of $\tilde O\left(K \sqrt{K N T}\left(1 + \frac{\sqrt{v_{\max}}}{q_{\min}}\text{OPT}\right) \right)$ under a mild assumption on the model parameters. In particular, our policy achieves a near-optimal $\tilde O(\sqrt{T})$ regret in the large inventory setting. Our policy builds upon the UCB-based approach for MNL-bandit without inventory constraints in [1] and addresses the inventory constraints through an exponentially sized LP for which we present a tractable approximation while keeping the $\tilde O(\sqrt{T})$ regret bound.