What game are we playing? End-to-end learning in normal and extensive form games

Ling, Chun Kai; Fang, F.; Kolter, J. Zico

doi:10.48550/arxiv.1805.02777

Cited by 15 publications

(27 citation statements)

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“…In recent years, there has been a great deal of interest in creating structured neural network layers that define implicit relationships between their inputs and outputs. For instance, such layers have been created for SAT solving (Wang et al, 2019), ordinary differential equations (Chen et al, 2018), normal and extensive-form games (Ling et al, 2018), rigid-body physics (de Avila Belbute-Peres et al, 2018), sequence modeling (Bai et al, 2019), and various classes of optimization problems Donti et al, 2017;Djolonga & Krause, 2017;Tschiatschek et al, 2018;Wilder et al, 2018;Gould et al, 2019). (Interestingly, softmax, sigmoid, and ReLU layers can also be viewed as implicit layers (Amos, 2019), though in practice it is more efficient to use their explicit form.)…”

Section: Related Workmentioning

confidence: 99%

DC3: A learning method for optimization with hard constraints

Donti,

Rolnick,

Kolter

2021

Preprint

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Large optimization problems with hard constraints arise in many settings, yet classical solvers are often prohibitively slow, motivating the use of deep networks as cheap "approximate solvers." Unfortunately, naive deep learning approaches typically cannot enforce the hard constraints of such problems, leading to infeasible solutions. In this work, we present Deep Constraint Completion and Correction (DC3), an algorithm to address this challenge. Specifically, this method enforces feasibility via a differentiable procedure, which implicitly completes partial solutions to satisfy equality constraints and unrolls gradient-based corrections to satisfy inequality constraints. We demonstrate the effectiveness of DC3 in both synthetic optimization tasks and the real-world setting of AC optimal power flow, where hard constraints encode the physics of the electrical grid. In both cases, DC3 achieves near-optimal objective values while preserving feasibility.

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Section: Related Workmentioning

confidence: 99%

DC3: A learning method for optimization with hard constraints

Donti,

Rolnick,

Kolter

2021

Preprint

Self Cite

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“…We consider the problem of predicting equilibria, given only contextual information, without knowing the players' cost functions. Although the players' cost functions are unknown, historical data pairs (d, x d ) can be utilized, consisting of contexts d and the resulting equilibrium x d [9,34,36,37,57]. This work proposes a new framework: Nash Fixed Point Networks (N-FPNs).…”

Section: Attributementioning

confidence: 99%

“…Thus, by construction, N-FPNs are implicit-depth models -neural networks containing an arbitrary number of layers [5,21,22,53] -and the operator weights can be efficiently trained using Jacobian-free backpropagation [21]. Importantly, N-FPNs can also avoid direct, costly projections onto sets of constraints for players' actions, which is the computational bottleneck of multiple prior works [34,36,37].…”

Section: Attributementioning

confidence: 99%

“…the set of players is finite) and certain nonatomic games, particularly traffic routing [45]. As pointed out in [34,36], learning to predict players' behaviours given the context is an important first step in manipulating the game towards a desirable outcome. For example, in traffic routing problems a central controller may seek to discourage motorists from over-utilizing a road through a quiet neighborhood.…”

Section: Attributementioning

confidence: 99%

“…Many recent works in deep learning have highlighted the power of using end-to-end learning in conjunction with known analytic models and constraints [9,13,16,30,34,36,37]. This best-of-both worlds approach fuses the flexibility of learning-based approaches with the interpretability of models derived by domain experts.…”

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confidence: 99%

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Learn to Predict Equilibria via Fixed Point Networks

Heaton¹,

McKenzie²,

Li³

et al. 2021

Preprint

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Systems of interacting agents can often be modeled as contextual games, where the context encodes additional information, beyond the control of any agent (e.g. weather for traffic and fiscal policy for market economies). In such systems, the most likely outcome is given by a Nash equilibrium. In many practical settings, only game equilibria are observed, while the optimal parameters for a game model are unknown. This work introduces Nash Fixed Point Networks (N-FPNs), a class of implicit-depth neural networks that output Nash equilibria of contextual games. The N-FPN architecture fuses data-driven modeling with provided constraints. Given equilibrium observations of a contextual game, N-FPN parameters are learnt to predict equilibria outcomes given only the context. We present an end-to-end training scheme for N-FPNs that is simple and memory efficient to implement with existing autodifferentiation tools. N-FPNs also exploit a novel constraint decoupling scheme to avoid costly projections. Provided numerical examples show the efficacy of N-FPNs on atomic and non-atomic games (e.g. traffic routing). 2 * Equal contribution 2 Codes are available on Github: github.com/howardheaton/nash_fixed_point_networks Preprint. Under review.

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Existence of Nash Equilibria on Integer Programming Games

Carvalho

Lodi

Pedroso

2018

Springer Proceedings in Mathematics &Amp; Statistics

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The recently defined class of integer programming games (IPG) models situations where multiple self-interested decision makers interact, with their strategy sets represented by a finite set of linear constraints together with integer requirements. Many real-world problems can suitably be fit in this class, and hence anticipating IPG outcomes is of crucial value for policy makers and regulators. Nash equilibria have been widely accepted as the solution concept of a game. Consequently, their computation provides a reasonable prediction of games outcome. In this paper, we start by showing the computational complexity of deciding the existence of a Nash equilibrium for an IPG. Then, using sufficient conditions for their existence, we develop two general algorithmic approaches that are guaranteed to approximate an equilibrium under mild conditions. We also showcase how our methodology can be changed to determine other equilibria definitions. The performance of our methods is analysed through computational experiments in a knapsack game, a competitive lot-sizing game and a kidney exchange game. To the best of our knowledge, this is the first time that equilibria computation methods for general integer programming games have been designed and computationally tested.

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What game are we playing? End-to-end learning in normal and extensive form games

Cited by 15 publications

References 0 publications

DC3: A learning method for optimization with hard constraints

DC3: A learning method for optimization with hard constraints

Learn to Predict Equilibria via Fixed Point Networks

Existence of Nash Equilibria on Integer Programming Games

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