A Variational Inequality Approach to Bayesian Regression Games

• URL: http://arxiv.org/abs/2103.13509v1
• Date: Wed, 24 Mar 2021 22:33:11 GMT
• Title: A Variational Inequality Approach to Bayesian Regression Games
• Authors: Wenshuo Guo, Michael I. Jordan, Tianyi Lin
• Abstract summary: We prove the existence of the uniqueness of a class of convex and generalize it to smooth cost functions. We provide two simple algorithms of solving them with necessarily strong convergence.
• Score: 90.79402153164587
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bayesian regression games are a special class of two-player general-sum Bayesian games in which the learner is partially informed about the adversary's objective through a Bayesian prior. This formulation captures the uncertainty in regard to the adversary, and is useful in problems where the learner and adversary may have conflicting, but not necessarily perfectly antagonistic objectives. Although the Bayesian approach is a more general alternative to the standard minimax formulation, the applications of Bayesian regression games have been limited due to computational difficulties, and the existence and uniqueness of a Bayesian equilibrium are only known for quadratic cost functions. First, we prove the existence and uniqueness of a Bayesian equilibrium for a class of convex and smooth Bayesian games by regarding it as a solution of an infinite-dimensional variational inequality (VI) in Hilbert space. We consider two special cases in which the infinite-dimensional VI reduces to a high-dimensional VI or a nonconvex stochastic optimization, and provide two simple algorithms of solving them with strong convergence guarantees. Numerical results on real datasets demonstrate the promise of this approach.

Related papers

• Convex Markov Games: A Framework for Fairness, Imitation, and Creativity in Multi-Agent Learning [31.958202912400925]
  We introduce the class of convex Markov games that allow general convex preferences over occupancy measures. Despite infinite time horizon and strictly higher generality than Markov games, pure strategy Nash equilibria exist under strict convexity. Our experiments imitate human choices in ultimatum games, reveal novel solutions to the repeated prisoner's dilemma, and find fair solutions in a repeated asymmetric coordination game.
  arXiv  Detail & Related papers  (2024-10-22T00:55:04Z)
• Pontryagin Neural Operator for Solving Parametric General-Sum Differential Games [24.012924492073974]
  We show that a Pontryagin-mode neural operator outperforms the current state-of-the-art hybrid PINN model on safety performance across games with parametric state constraints. Our key contribution is the introduction of a costate loss defined on the discrepancy between forward and backward costate rollouts. We show that the costate dynamics, which can reflect state constraint violation, effectively enables the learning of differentiable values with large Lipschitz constants.
  arXiv  Detail & Related papers  (2024-01-03T02:15:32Z)
• Offline Learning in Markov Games with General Function Approximation [22.2472618685325]
  We study offline multi-agent reinforcement learning (RL) in Markov games. We provide the first framework for sample-efficient offline learning in Markov games.
  arXiv  Detail & Related papers  (2023-02-06T05:22:27Z)
• Global Nash Equilibrium in Non-convex Multi-player Game: Theory and Algorithms [66.8634598612777]
  We show that Nash equilibrium (NE) is acceptable to all players in a multi-player game. We also show that no one can benefit unilaterally from the general theory step by step.
  arXiv  Detail & Related papers  (2023-01-19T11:36:50Z)
• Stochastic Gradient Descent-Ascent and Consensus Optimization for Smooth Games: Convergence Analysis under Expected Co-coercivity [49.66890309455787]
  We introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO. We prove linear convergence of both methods to a neighborhood of the solution when they use constant step-size. Our convergence guarantees hold under the arbitrary sampling paradigm, and we give insights into the complexity of minibatching.
  arXiv  Detail & Related papers  (2021-06-30T18:32:46Z)
• Preference learning along multiple criteria: A game-theoretic perspective [97.94912276610002]
  We generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability. Our framework allows for non-linear aggregation of preferences across criteria, and generalizes the linearization-based approach from multi-objective optimization. We show that the Blackwell winner of a multi-criteria problem instance can be computed as the solution to a convex optimization problem.
  arXiv  Detail & Related papers  (2021-05-05T03:23:11Z)
• VIB is Half Bayes [80.3767111908235]
  We show that the Variational Information Bottleneck can be viewed as a compromise between fully empirical and fully Bayesian objectives. We argue that this approach provides some of the benefits of Bayes while requiring only some of the work.
  arXiv  Detail & Related papers  (2020-11-17T15:36:35Z)
• Online and Distribution-Free Robustness: Regression and Contextual Bandits with Huber Contamination [29.85468294601847]
  We revisit two classic high-dimensional online learning problems, namely linear regression and contextual bandits. We show that our algorithms succeed where conventional methods fail.
  arXiv  Detail & Related papers  (2020-10-08T17:59:05Z)
• Stochastic Hamiltonian Gradient Methods for Smooth Games [51.47367707388402]
  We focus on the class of Hamiltonian methods and provide the first convergence guarantees for certain classes of smooth games. Using tools from the optimization literature we show that SHGD converges linearly to the neighbourhood of a gradient. Our results provide the first global non-asymotic last-rate convergence guarantees for the class of general games.
  arXiv  Detail & Related papers  (2020-07-08T15:42:13Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.