Study best-response learning dynamics in zero-sum polymatrix games under full and minimal information settings.
problem Learning dynamics in zero-sum polymatrix games under different information settings.
method Two-timescale learning dynamics combining smoothed best-response updates and TD-learning for estimating local payoff functions.
result Polynomial-time finite-sample guarantees for convergence to an ε-Nash equilibrium in the minimal information case.
Paper introduces metrics for evaluating multi-agent policies using best response dynamics.
problem Evaluation and ranking of multi-agent policies in reinforcement learning.
method Adopting strict best response dynamics (SBRD) to model selfish behaviors, proposing perturbed SBRD for dynamic and non-stationary settings.
result Proposed perturbed SBRD can observe policies with maximum metrics and differ from optimal by any given tolerance.
Neural operators approximate Stackelberg game solutions.
problem Intractability of follower's best-response operator in dynamic Stackelberg games.
method Used attention-based neural operators to approximate the best-response operator.
result Approximate best-response operator yields close game value.
New algorithm for solving minimax problems over distributions converges to Nash equilibrium.
problem Solving minimax problems over probability distributions.
method Symmetric Mean-field Langevin Dynamics (MFL-AG and MFL-ABR) with weighted averaging and best response dynamics.
result Converges to mixed Nash equilibrium with average-iterate and last-iterate convergence.
Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters …
Study of portfolio management under relative performance concerns using mean field games.
problem Portfolio management problems under relative performance concerns.
method Forward utilities of CARA type, mean field games, best response and equilibrium strategies.
result Solve forward-utility finite player game and mean-field game under asset specialization.
Investors' strategic trading affects asset prices, modeled as a game.
problem Investors' trading rates influence asset prices in dynamic markets.
method Model as a non-zero sum singular stochastic differential game, establishing equivalence between best-response and auxiliary control problems.
result Unique Nash equilibrium is deterministic with a closed-form solution.
New algorithms achieve decision calibration without sample complexity dependent on feature dimension.
problem Achieving decision calibration for nonlinear loss functions with polynomial sample complexity.
method Developed smooth relaxation of decision calibration, enabling dimension-free algorithms.
result Efficient algorithms post-process predictors to satisfy decision calibration without worsening accuracy.
ISMCTS-BR learns best responses in large games, approximating worst-case performance.
problem Learning robustness to worst-case outcomes in large games.
method ISMCTS-BR, a scalable search-based algorithm for deep reinforcement learning.
result ISMCTS-BR approximates worst-case performance in large games.
New method for sparse kernel selection improves prediction accuracy.
problem Sparse Multiple Kernel Learning for binary classification.
method Alternating best response algorithm with semidefinite relaxations.
result Method outperforms state-of-the-art MKL approaches in prediction accuracy.
Improved hypernetwork for efficient neural network hyperparameter tuning.
problem Efficiently optimizing hyperparameters in neural networks.
method Proposed Δ-STN architecture focusing on accurate best-response Jacobian approximation. result Significantly improved hyperparameter tuning accuracy and stability.
Deep RL improves Diplomacy performance, outperforming previous methods.
problem Applying RL to complex, many-agent, simultaneous-move games like Diplomacy.
method Best response policy iteration and fictitious play approximation.
result Deep RL agents convincingly outperform previous Diplomacy agents.
Paper studies zero-sum games with noisy observations and identifies equilibrium conditions.
problem Zero-sum games with noisy observations of the leader's actions.
method Analyzes the equilibrium of games with noisy action observability, identifies necessary conditions for uniqueness, and investigates the cardinality of best responses.
result The noisy observations significantly impact the cardinality of the follower's set of best responses, and under certain conditions, this set becomes a singleton almost surely.
In this paper, we propose a convergent parallel best-response algorithm with the exact line search for the nondifferentiable nonconvex sparsity-regularized rank minimization problem. On the one hand, it exhibits a faster convergence than subgradient algorithms and block coordinate descent algorithms. On the other hand,…
Modeling dynamic groundwater markets with price formation and trading strategies.
problem Understanding competitive effects in environmental markets with groundwater banking.
method Stochastic models and game theory with machine learning algorithms.
result Sub-game perfect Nash equilibria characterized by groundwater price processes.
New algorithms achieve logarithmic regret in KL-regularized Markov games.
problem Improving sample efficiency in game-theoretic settings with KL regularization.
method Developed OMG and SOMG algorithms for matrix and Markov games, using best response sampling and superoptimistic bonuses.
result Logarithmic regret in T that scales inversely with KL regularization strength β. Algorithm solves online binary classification and infinite games using ERM oracle.
problem Online learning and solving infinite games with computationally inefficient oracles.
method Proposes an algorithm relying solely on ERM oracle calls for online binary classification and nonparametric games.
result Achieves finite and sublinearly growing regret in various settings.
Heterogeneous SVO leads to diverse policies in sequential social dilemmas.
problem Understanding how diverse social value orientations affect behavior in sequential social dilemmas.
method Extending prior reinforcement learning studies, we instantiated heterogeneous SVO in a sequential social dilemma setting and measured task-specific diversity metrics.
result Heterogeneous SVO leads to meaningfully diverse policies across various incentive structures.
A multi-layer deep Gaussian process (DGP) model is a hierarchical composition of GP models with a greater expressive power. Exact DGP inference is intractable, which has motivated the recent development of deterministic and stochastic approximation methods. Unfortunately, the deterministic approximation methods yield a…
NeuPL learns diverse policies in strategy games efficiently.
problem Iterative training of policies in strategy games leads to under-trained good-responses and wasteful repetition.
method NeuPL uses a single conditional model to represent a population of policies, offering convergence guarantees and transfer learning.
result NeuPL achieves better performance and efficiency across various domains, enabling access to novel strategies.
Study examines large banks' role in interbank markets using game theory.
problem Understanding systemic risk in interbank markets with large banks.
method Mean-field game framework, convex analysis, Monte Carlo simulations.
result Large banks can positively or negatively impact market stability.
New method improves robustness in partially observable domains by training against latent distribution shifts.
problem Challenges in robustness under latent distribution shift in partially observable reinforcement learning.
method Formalizes adversarial latent-initial-state POMDP, proves minimax principle, derives best-response inequalities.
result Reduces robustness gaps from 10.3 to 3.1 shots with targeted exposure to shifted latent distributions.
Generative Adversarial Networks (GAN) have become one of the most successful frameworks for unsupervised generative modeling. As GANs are difficult to train much research has focused on this. However, very little of this research has directly exploited game-theoretic techniques. We introduce Generative Adversarial Netw…
The paper analyzes performance criteria for competing fund managers in Ito-diffusion markets.
problem Analyzing performance of competing fund managers in Ito-diffusion markets.
method Developed forward relative performance criteria and forward Nash equilibrium for passive and competitive cases.
result Extended performance criteria for investment problems in Ito-diffusion markets.
Learning by experience in Multi-Agent Systems (MAS) is a difficult and exciting task, due to the lack of stationarity of the environment, whose dynamics evolves as the population learns. In order to design scalable algorithms for systems with a large population of interacting agents (e.g. swarms), this paper focuses on…
Stochastic games provide a framework for interactions among multiple agents and enable a myriad of applications. In these games, agents decide on actions simultaneously, the state of every agent moves to the next state, and each agent receives a reward. However, finding an equilibrium (if exists) in this game is often …
Study of LQ MFGs in infinite-dimensional Hilbert spaces.
problem Mean field games in infinite-dimensional settings with stochastic dynamics.
method Analysis of coupled semilinear infinite-dimensional stochastic evolution equations, development of Nash equilibrium.
result Characterization of unique Nash equilibrium in the limit of many agents.
New method finds all Nash equilibria via vector optimization.
problem Finding all Nash equilibria in games.
method Formulate vector optimization problem to find Pareto optimal solutions.
result Characterize set of all Nash equilibria as Pareto optimal solutions.
New RL algorithms find SNE in Markov games with myopic followers.
problem Finding SNE in Markov games with myopic followers.
method Optimistic and pessimistic variants of least-squares value iteration, incorporating function approximation.
result First provably efficient RL algorithms for SNEs in general-sum Markov games with myopic followers.
We present a simple dynamic equilibrium model for an online exchange where both buyers and sellers arrive according to a exogenously defined stochastic process. The structure of this exchange is motivated by the limit order book mechanism used in stock markets. Both buyers and sellers are elastic in the price-quantity …
The standard risk minimization paradigm of machine learning is brittle when operating in environments whose test distributions are different from the training distribution due to spurious correlations. Training on data from many environments and finding invariant predictors reduces the effect of spurious features by co…
Develops variational framework for LQG risk-sensitive MFGs with major-minor interactions.
problem Risk-sensitive optimal control in LQG systems with major-minor interactions.
method Variational approach, nonlinear necessary and sufficient condition of optimality, equivalent risk-neutral measure, Markovian closed-loop best-response strategies.
result Derives optimal control strategies for LQG risk-sensitive MFGs with major-minor interactions, establishing Nash and ε-Nash equilibria. Fictitious play is a simple and widely studied adaptive heuristic for playing repeated games. It is well known that fictitious play fails to be Hannan consistent. Several variants of fictitious play including regret matching, generalized regret matching and smooth fictitious play, are known to be Hannan consistent. In …
We address the challenge of designing optimal adversarial noise algorithms for settings where a learner has access to multiple classifiers. We demonstrate how this problem can be framed as finding strategies at equilibrium in a two-player, zero-sum game between a learner and an adversary. In doing so, we illustrate the…
The paper analyzes optimal stock position-building strategies in competitive markets.
problem Optimal stock position-building in competitive markets with market impact.
method Developed a game-theoretic framework to find best-response strategies.
result Closed-form solutions for equilibrium trading strategies were derived.
Hybrid Policy Optimization tackles reinforcement learning in hybrid spaces, improving performance over PPO.
problem Credit assignment issues and biased gradients in hybrid discrete-continuous action spaces.
method Mixed gradient estimator combining pathwise and score-function gradients, reformulating problems in hybrid form.
result HPO substantially outperforms PPO on inventory control and switched systems, with performance gaps increasing with continuous action dimension.
Novel approximation hierarchy for sparse quadratic programs.
problem Sparse Quadratic Programs with Cardinality Constraints.
method Exploits rank-dominating eigenvectors for min-max optimization over binary variables.
result Efficient screening of nonzero elements with scalable optimization algorithms.
The large majority of risk-sharing transactions involve few agents, each of whom can heavily influence the structure and the prices of securities. This paper proposes a game where agents' strategic sets consist of all possible sharing securities and pricing kernels that are consistent with Arrow-Debreu sharing rules. F…
We study the problem of learning classifiers robust to universal adversarial perturbations. While prior work approaches this problem via robust optimization, adversarial training, or input transformation, we instead phrase it as a two-player zero-sum game. In this new formulation, both players simultaneously play the s…
Generative adversarial networks (GANs) are powerful tools for learning generative models. In practice, the training may suffer from lack of convergence. GANs are commonly viewed as a two-player zero-sum game between two neural networks. Here, we leverage this game theoretic view to study the convergence behavior of the…
New algorithms improve on bandit feedback in matrix games with unknown payoff matrices.
problem Improving performance in matrix games with unknown payoff matrices and bandit feedback.
method Regret analyses of variants of UCB and K-learning.
result New algorithms achieve lower regret compared to adversarial bandit algorithms.
Pure exploration (aka active testing) is the fundamental task of sequentially gathering information to answer a query about a stochastic environment. Good algorithms make few mistakes and take few samples. Lower bounds (for multi-armed bandit models with arms in an exponential family) reveal that the sample complexity …
Following the recent literature on make take fees policies, we consider an exchange wishing to set a suitable contract with several market makers in order to improve trading quality on its platform. To do so, we use a principal-agent approach, where the agents (the market makers) optimise their quotes in a Nash equilib…
Algorithm converges to Nash equilibria in competitive games.
problem Finding Nash equilibria in decentralized, competitive Markov games.
method Decentralized Optimistic Gradient Descent/Ascent with a critic.
result Converges to the set of Nash equilibria under self-play.
Study online learning in unknown Markov games with sublinear regret.
problem Online learning in unknown Markov games with unobservable opponents.
method Introduced an algorithm achieving sublinear regret against the minimax value.
result First sublinear regret bound for unknown Markov games, independent of action spaces size.
Investors usually resort to financial advisors to improve their investment process until the point of complete delegation on investment decisions. Surely, financial advice is potentially a correcting factor in investment decisions but, in the past, the media and regulators blamed biased advisors for manipulating the ex…
In this paper the problem of optimal derivative design, profit maximization and risk minimization under adverse selection when multiple agencies compete for the business of a continuum of heterogenous agents is studied. The presence of ties in the agents' best-response correspondences yields discontinuous payoff functi…
Plug-in method improves performative prediction accuracy.
problem Learning under performative feedback with slow convergence rates.
method Plug-in performative optimization using models.
result Plug-in method can be superior to model-agnostic strategies.