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The paper studies the application of first-order methods to the problem of computing equilibria of large-scale extensive-form games. It introduces a new weighted entropy-based distance-generating function for instantiating first-order methods. The new function achieves significantly better strong-convexity properties than existing weight schemes for the dilated entropy while maintaining the same easily implemented closed-form proximal mapping as the prior state of the art. The paper then generalizes our new entropy distance function, as well as the whole class of dilated distance functions, to the scaled extension operator. This yields the first efficiently computable distance-generating function for the decision polytopes capturing correlated and team solution concepts for extensive-form games. By instantiating first-order methods with these regularizers, several new results are achieved, such as the first method for computing ex ante correlated team equilibria with a guaranteed 1/T rate of convergence and efficient proximal updates. 

The design of multi-item, multi-bidder auctions involves a delicate balancing act of economic objectives, bidder incentives, and real-world complexities. Efficient auctions, that is, auctions that allocate items to maximize total bidder value, are practically desirable since they promote the most economically beneficial use of resources. Arguably the biggest drawback of efficient auctions, however, is their potential to generate very low revenue. In this work, we show how the auction designer can artificially inject competition into the auction to boost revenue while striving to maintain efficiency. First, we invent a new auction family that enables the auction designer to specify competition in a precise, expressive, and interpretable way. We then introduce a new model of bidder behavior and individual rationality to understand how bidders act when prices are too competitive. Next, under our bidder behavior model, we use our new competitive auction class to derive the globally revenue-optimal efficient auction under two different knowledge models for the auction designer: knowledge of full bidder value distributions and knowledge of bidder value quantiles. Finally, we study a third knowledge model for the auction designer: knowledge of historical bidder valuation data. In this setting we present sample and computationally efficient learning algorithms that find high-revenue probably-efficient competitive auctions from bidder data. Our learning algorithms are instance adaptive and can be run in parallel across bidders, unlike most prior approaches to data-driven auction design. 

Coalition structure generation (CSG), i.e. the problem of optimally partitioning a set of agents into coalitions to maximize social welfare, is a fundamental computational problem in multiagent systems. This problem is important for many applications where small run times are necessary, including transportation and disaster response. In this paper, we develop SALDAE, a multiagent path finding algorithm for CSG that operates on a graph of coalition structures. Our algorithm utilizes a variety of heuristics and strategies to perform the search and guide it. It is an anytime algorithm that can handle large problems with hundreds and thousands of agents. We show empirically on nine standard value distributions, including disaster response and electric vehicle allocation benchmarks, that our algorithm enables a rapid finding of high-quality solutions and compares favorably with other state-of-the-art methods. 

Algorithms often have tunable parameters that impact performance metrics such as runtime and solution quality. For many algorithms used in practice, no parameter settings admit meaningful worst-case bounds, so the parameters are made available for the user to tune. Alternatively, parameters may be tuned implicitly within the proof of a worst-case approximation ratio or runtime bound. Worst-case instances, however, may be rare or nonexistent in practice. A growing body of research has demonstrated that a data-driven approach to parameter tuning can lead to significant improvements in performance. This approach uses atraining setof problem instances sampled from an unknown, application-specific distribution and returns a parameter setting with strong average performance on the training set. We provide techniques for derivinggeneralization guaranteesthat bound the difference between the algorithm’s average performance over the training set and its expected performance on the unknown distribution. Our results apply no matter how the parameters are tuned, be it via an automated or manual approach. The challenge is that for many types of algorithms, performance is a volatile function of the parameters: slightly perturbing the parameters can cause a large change in behavior. Prior research [e.g.,12,16,20,62] has proved generalization bounds by employing case-by-case analyses of greedy algorithms, clustering algorithms, integer programming algorithms, and selling mechanisms. We streamline these analyses with a general theorem that applies whenever an algorithm’s performance is a piecewise-constant, piecewise-linear, or—more generally—piecewise-structuredfunction of its parameters. Our results, which are tight up to logarithmic factors in the worst case, also imply novel bounds for configuring dynamic programming algorithms from computational biology.