no code implementations • 9 Jun 2016 • Christian Kroer, Miroslav Dudík, Sébastien Lahaie, Sivaraman Balakrishnan
We present a new combinatorial market maker that operates arbitrage-free combinatorial prediction markets specified by integer programs.
no code implementations • 16 Feb 2017 • Christian Kroer, Kevin Waugh, Fatma Kilinc-Karzan, Tuomas Sandholm
By introducing a new weighting scheme for the dilated entropy function, we develop the first distance-generating function for the strategy spaces of sequential games that has no dependence on the branching factor of the player.
no code implementations • 22 Jun 2017 • Vincent Conitzer, Christian Kroer, Eric Sodomka, Nicolas E. Stier-Moses
Although we show that computing either a social-welfare-maximizing or a revenue-maximizing pacing equilibrium is NP-hard, we present a mixed-integer program (MIP) that can be used to find equilibria optimizing several relevant objectives.
Computer Science and Game Theory
no code implementations • ICML 2017 • Gabriele Farina, Christian Kroer, Tuomas Sandholm
We use an instantiation of the CFR framework to develop algorithms for solving behaviorally-constrained (and, as a special case, perturbed in the Selten sense) extensive-form games, which allows us to compute approximate Nash equilibrium refinements.
no code implementations • 21 Nov 2017 • Christian Kroer, Gabriele Farina, Tuomas Sandholm
We then extend the program to the robust setting for Stackelberg equilibrium under unlimited and under limited lookahead by the opponent.
no code implementations • 10 Sep 2018 • Gabriele Farina, Christian Kroer, Tuomas Sandholm
Experiments show that our framework leads to algorithms that scale at a rate comparable to the fastest variants of counterfactual regret minimization for computing Nash equilibrium, and therefore our approach leads to the first algorithm for computing quantal response equilibria in extremely large games.
no code implementations • NeurIPS 2018 • Christian Kroer, Gabriele Farina, Tuomas Sandholm
We present, to our knowledge, the first GPU implementation of a first-order method for extensive-form games.
no code implementations • 6 Nov 2018 • Gabriele Farina, Christian Kroer, Tuomas Sandholm
We show that local regret minimizers for the simpler sets can be combined with additional regret minimizers into an aggregate regret minimizer for the composite set.
no code implementations • NeurIPS 2018 • Christian Kroer, Tuomas Sandholm
In this paper we present a unified framework for analyzing abstractions that can express all types of abstractions and solution concepts used in prior papers with performance guarantees---while maintaining comparable bounds on abstraction quality.
no code implementations • 18 Jan 2019 • Christian Kroer, Alexander Peysakhovich, Eric Sodomka, Nicolas E. Stier-Moses
Computing market equilibria is an important practical problem for market design, for example in fair division of items.
no code implementations • 13 Feb 2019 • Gabriele Farina, Christian Kroer, Noam Brown, Tuomas Sandholm
The CFR framework has been a powerful tool for solving large-scale extensive-form games in practice.
no code implementations • 17 Feb 2019 • Christian Kroer, Tuomas Sandholm
We characterize the hardness of finding a Nash equilibrium or an optimal commitment strategy for either player, showing that in some of these variations the problem can be solved in polynomial time while in others it is PPAD-hard, NP-hard, or inapproximable.
no code implementations • 26 Mar 2019 • Yuan Gao, Christian Kroer, Donald Goldfarb
In particular, the increasing averages consistently outperform the uniform averages in all test problems by orders of magnitude.
no code implementations • NeurIPS 2019 • Alexander Peysakhovich, Christian Kroer, Adam Lerer
We consider the problem of using logged data to make predictions about what would happen if we changed the `rules of the game' in a multi-agent system.
no code implementations • 6 Jun 2019 • Alexander Peysakhovich, Christian Kroer
We consider the problem of dividing items between individuals in a way that is fair both in the sense of distributional fairness and in the sense of not having disparate impact across protected classes.
no code implementations • NeurIPS 2019 • Gabriele Farina, Christian Kroer, Tuomas Sandholm
Our algorithms provably converge at a rate of $T^{-1}$, which is superior to prior counterfactual regret minimization algorithms.
no code implementations • ICML 2020 • Gabriele Farina, Christian Kroer, Tuomas Sandholm
Our framework allows us to instantiate several new stochastic methods for solving sequential games.
no code implementations • 11 May 2020 • Julien Grand-Clément, Christian Kroer
Our framework is also the first one to solve robust MDPs with $s$-rectangular KL uncertainty sets.
no code implementations • NeurIPS 2020 • Tom Yan, Christian Kroer, Alexander Peysakhovich
We apply our methods to study teams of artificial RL agents as well as real world teams from professional sports.
no code implementations • 21 Jul 2020 • Steven Yin, Shatian Wang, Lingyi Zhang, Christian Kroer
Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities.
no code implementations • 28 Jul 2020 • Gabriele Farina, Christian Kroer, Tuomas Sandholm
In spite of this prevalence, the regret matching (RM) and regret matching+ (RM+) algorithms have been preferred in the practice of solving large-scale games (as the local regret minimizers within the counterfactual regret minimization framework).
no code implementations • 27 May 2021 • Gabriele Farina, Christian Kroer, Tuomas Sandholm
The scaled extension operator is a way to recursively construct convex sets, which generalizes the decision polytope of extensive-form games, as well as the convex polytopes corresponding to correlated and team equilibria.
no code implementations • NeurIPS 2021 • Julien Grand-Clément, Christian Kroer
We develop new parameter-free and scale-free algorithms for solving convex-concave saddle-point problems.
no code implementations • NeurIPS 2021 • Chung-Wei Lee, Christian Kroer, Haipeng Luo
Inspired by recent advances on last-iterate convergence of optimistic algorithms in zero-sum normal-form games, we study this phenomenon in sequential games, and provide a comprehensive study of last-iterate convergence for zero-sum extensive-form games with perfect recall (EFGs), using various optimistic regret-minimization algorithms over treeplexes.
no code implementations • 10 Aug 2021 • Duncan C McElfresh, Christian Kroer, Sergey Pupyrev, Eric Sodomka, Karthik Sankararaman, Zack Chauvin, Neil Dexter, John P Dickerson
Using the Facebook Blood Donation tool, we conduct the first large-scale algorithmic matching of blood donors with donation opportunities.
no code implementations • 29 Sep 2021 • Ioannis Anagnostides, Gabriele Farina, Christian Kroer, Tuomas Sandholm
A recent emerging trend in the literature on learning in games has been concerned with providing accelerated learning dynamics for correlated and coarse correlated equilibria in normal-form games.
no code implementations • 1 Feb 2022 • Gabriele Farina, Chung-Wei Lee, Haipeng Luo, Christian Kroer
In this paper we show that the Optimistic Multiplicative Weights Update (OMWU) algorithm -- the premier learning algorithm for NFGs -- can be simulated on the normal-form equivalent of an EFG in linear time per iteration in the game tree size using a kernel trick.
no code implementations • 18 Feb 2022 • Santiago Balseiro, Christian Kroer, Rachitesh Kumar
Moreover, we provide an online algorithm that always achieves performance on this Pareto frontier.
no code implementations • 24 Feb 2022 • Julien Grand-Clément, Christian Kroer
We introduce the Conic Blackwell Algorithm$^+$ (CBA$^+$) regret minimizer, a new parameter- and scale-free regret minimizer for general convex sets.
no code implementations • 28 Feb 2022 • Andrea Celli, Matteo Castiglioni, Christian Kroer
We study online learning problems in which a decision maker wants to maximize their expected reward without violating a finite set of $m$ resource constraints.
no code implementations • 25 Apr 2022 • Ioannis Anagnostides, Gabriele Farina, Christian Kroer, Chung-Wei Lee, Haipeng Luo, Tuomas Sandholm
In this paper we establish efficient and \emph{uncoupled} learning dynamics so that, when employed by all players in a general-sum multiplayer game, the \emph{swap regret} of each player after $T$ repetitions of the game is bounded by $O(\log T)$, improving over the prior best bounds of $O(\log^4 (T))$.
3 code implementations • 12 Jun 2022 • Samuel Sokota, Ryan D'Orazio, J. Zico Kolter, Nicolas Loizou, Marc Lanctot, Ioannis Mitliagkas, Noam Brown, Christian Kroer
This work studies an algorithm, which we call magnetic mirror descent, that is inspired by mirror descent and the non-Euclidean proximal gradient algorithm.
no code implementations • 17 Jun 2022 • Gabriele Farina, Ioannis Anagnostides, Haipeng Luo, Chung-Wei Lee, Christian Kroer, Tuomas Sandholm
In this paper, we answer this in the positive by establishing the first uncoupled learning algorithm with $O(\log T)$ per-player regret in general \emph{convex games}, that is, games with concave utility functions supported on arbitrary convex and compact strategy sets.
no code implementations • 27 Jun 2022 • Santiago Balseiro, Christian Kroer, Rachitesh Kumar
We go on to give a fast algorithm for computing a schedule of target consumption rates that leads to near-optimal performance in the unknown-horizon setting.
1 code implementation • 15 Sep 2022 • Sai Mali Ananthanarayanan, Christian Kroer
In the security setting, the goal is for the leader to compute an optimal strategy to commit to, in order to protect some asset.
no code implementations • 25 Sep 2022 • Steven Yin, Christian Kroer
We consider the problem of allocating a distribution of items to $n$ recipients where each recipient has to be allocated a fixed, prespecified fraction of all items, while ensuring that each recipient does not experience too much envy.
no code implementations • 29 Sep 2022 • Luofeng Liao, Yuan Gao, Christian Kroer
In resource allocation, it is crucial to quantify the variability of the resource received by the agents (such as blood banks and food banks) in addition to fairness and efficiency properties of the systems.
no code implementations • 2 Feb 2023 • Matteo Castiglioni, Andrea Celli, Christian Kroer
Finally, we show how to instantiate the framework to optimally bid in various mechanisms of practical relevance, such as first- and second-price auctions.
no code implementations • 1 Nov 2023 • Yang Cai, Gabriele Farina, Julien Grand-Clément, Christian Kroer, Chung-Wei Lee, Haipeng Luo, Weiqiang Zheng
Algorithms based on regret matching, specifically regret matching$^+$ (RM$^+$), and its variants are the most popular approaches for solving large-scale two-player zero-sum games in practice.