Thomas Lavastida

Michael Dinitz, Sungjin Im, Thomas Lavastida et al. · cmu

The research area of algorithms with predictions has seen recent success showing how to incorporate machine learning into algorithm design to improve performance when the predictions are correct, while retaining worst-case guarantees when they are not. Most previous work has assumed that the algorithm has access to a single predictor. However, in practice, there are many machine learning methods available, often with incomparable generalization guarantees, making it hard to pick a best method a priori. In this work we consider scenarios where multiple predictors are available to the algorithm and the question is how to best utilize them. Ideally, we would like the algorithm's performance to depend on the quality of the best predictor. However, utilizing more predictions comes with a cost, since we now have to identify which prediction is the best. We study the use of multiple predictors for a number of fundamental problems, including matching, load balancing, and non-clairvoyant scheduling, which have been well-studied in the single predictor setting. For each of these problems we introduce new algorithms that take advantage of multiple predictors, and prove bounds on the resulting performance.

Titing Cui, Su Jia, Thomas Lavastida · cmu

Dynamic pricing models often posit that a $\textbf{stream}$ of customer interactions occur sequentially, where customers' valuations are drawn independently. However, this model is not entirely reflective of the real world, as it overlooks a critical aspect, the law of diminishing marginal utility, which states that a customer's marginal utility from each additional unit declines. This causes the valuation distribution to shift towards the lower end, which is not captured by the stream model. This motivates us to study a pool-based model, where a $\textbf{pool}$ of customers repeatedly interacts with a monopolist seller, each of whose valuation diminishes in the number of purchases made according to a discount function. In particular, when the discount function is constant, our pool model recovers the stream model. We focus on the most fundamental special case, where a customer's valuation becomes zero once a purchase is made. Given $k$ prices, we present a non-adaptive, detail-free (i.e., does not "know" the valuations) policy that achieves a $1/k$ competitive ratio, which is optimal among non-adaptive policies. Furthermore, based on a novel debiasing technique, we propose an adaptive learn-then-earn policy with a $\tilde O(k^{2/3} n^{2/3})$ regret.

Gerdus Benadè, Rathish Das, Thomas Lavastida

Combinatorial multi-armed bandits provide a fundamental online decision-making environment where a decision-maker interacts with an environment across $T$ time steps, each time selecting an action and learning the cost of that action. The goal is to minimize regret, defined as the loss compared to the optimal fixed action in hindsight under full-information. There has been substantial interest in leveraging what is known about offline algorithm design in this online setting. Offline greedy and linear optimization algorithms (both exact and approximate) have been shown to provide useful guarantees when deployed online. We investigate local search methods, a broad class of algorithms used widely in both theory and practice, which have thus far been under-explored in this context. We focus on problems where offline local search terminates in an approximately optimal solution and give a generic method for converting such an offline algorithm into an online stochastic combinatorial bandit algorithm with $O(\log^3 T)$ (approximate) regret. In contrast, existing offline-to-online frameworks yield regret (and approximate regret) which depend sub-linearly, but polynomially on $T$. We demonstrate the flexibility of our framework by applying it to three online stochastic combinatorial optimization problems: scheduling to minimize total completion time, finding a minimum cost base of a matroid and uncertain clustering.

Michael Dinitz, Sungjin Im, Thomas Lavastida et al.

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a distribution. We initiate the study of algorithms with distributional predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \log η)$, where $H(p)$ is the entropy of the true distribution $p$ and $η$ is the earth mover's distance between $p$ and the predicted distribution $\hat p$. This also yields the first distributionally-robust algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.

Michael Dinitz, Sungjin Im, Thomas Lavastida et al.

A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in the design of competitive online algorithms. However, the question of improving algorithm running times with predictions has largely been unexplored. We take a first step in this direction by combining the idea of machine-learned predictions with the idea of "warm-starting" primal-dual algorithms. We consider one of the most important primitives in combinatorial optimization: weighted bipartite matching and its generalization to $b$-matching. We identify three key challenges when using learned dual variables in a primal-dual algorithm. First, predicted duals may be infeasible, so we give an algorithm that efficiently maps predicted infeasible duals to nearby feasible solutions. Second, once the duals are feasible, they may not be optimal, so we show that they can be used to quickly find an optimal solution. Finally, such predictions are useful only if they can be learned, so we show that the problem of learning duals for matching has low sample complexity. We validate our theoretical findings through experiments on both real and synthetic data. As a result we give a rigorous, practical, and empirically effective method to compute bipartite matchings.