GP-MRO discovers robust mixed strategies for unknown objectives.
problem Optimizing unknown objectives against worst-case uncertain parameters.
method Sequential learning from noisy point evaluations, combining online learning and Gaussian processes.
result GP-MRO finds robust mixed strategies that significantly improve performance over deterministic strategies.
No-regret learning fails to converge to Nash equilibria in mixed strategies.
problem Limiting behavior of mixed strategies in repeated games.
method Study of optimal no-regret learning algorithms for 2x2 competitive games.
result Limiting mixed strategies cannot converge to Nash equilibria under mean-based and monotonic updates.
New findings show pure strategy equilibria are more robust in a war of attrition game.
problem Analyzing a game of war of attrition under complete information.
method Examined the stability of equilibria in pure and mixed strategies under varying payoffs.
result Pure strategy equilibria are more robust to perturbations of the canonical model.
Investigates market dynamics with informed traders and high-frequency traders.
problem Trading large orders in a market with multiple high-frequency traders.
method Analyzes a three-period Kyle's model with a normal-speed informed trader and multiple anticipatory high-frequency traders under different inventory pressures.
result Surprising results: improving HFTs' speed or prediction can harm them but benefit the informed trader.
A human-like strategy improves DRL performance in Atari games.
problem Lack of exploration in DRL for high-dimensional problems.
method Mixed strategy approach mimicking human behavior.
result Higher maximum score probability achieved in Breakout game.
Framework improves answer quality for diverse question phrasings.
problem Different phrasings of similar questions lead to varying answer quality.
method Constrained Mixed-Strategy GroupDRO for optimizing system-prompt weights.
result Reduces worst-case quality loss by 13.7% across metrics and groups.
By generalizing the measurements on the game experiments of mixed strategy Nash equilibrium, we study the dynamical pattern in a representative dynamic stochastic general equilibrium (DSGE). The DSGE model describes the entanglements of the three variables (output gap [y], inflation [π] and nominal interest rate [$…
SAP prunes activations to defend against adversarial examples.
problem Vulnerability of neural networks to adversarial examples.
method SAP uses a stochastic mixed strategy to prune activations.
result SAP improves accuracy and preserves calibration against adversarial attacks.
New adaptive NMF methods improve recommendation accuracy.
problem Improving recommendation accuracy in recommender systems.
method Adaptive Nonnegative Matrix Factorization (NMF) with mixed strategies.
result New algorithms outperform classical methods in reconstruction of missing ratings.
A game theory study on optimal hiding and searching strategies in discrete locations.
problem Optimal hiding and searching strategies in a two-person zero-sum game between a hider and a searcher.
method Proved the existence of optimal strategies, developed an algorithm to compute them, and compared with a simple strategy.
result Optimal hiding strategy involves hiding in each location with nonzero probability, and optimal searching strategy can be constructed with up to n simple sequences.
The paper develops a new algorithm for constructing minimax estimators using online learning techniques.
problem Designing minimax estimators for probability distribution parameters.
method Viewing the problem as a zero-sum game and using online learning with non-convex losses to find a Nash equilibrium.
result The algorithm constructs both a minimax estimator and a least favorable prior.
A game theory study examines gradual concessions in variable contribution games under uncertainty.
problem Gradualism in contribution games due to free rider effect.
method Stochastic game analysis of variable contribution games, extending Nerlove-Arrow model.
result Equilibrium characterized by regular control strategies leading to gradual concession.
Given a multifunction from X to the k−fold symmetric product Symk(X), we use the Dold-Thom Theorem to establish a homological selection Theorem. This is used to establish existence of Nash equilibria. Cost functions in problems concerning the existence of Nash Equilibria are traditionally multilinear in the mixe…
Introduces GANGs to model GANs as games, solving them with RB-NE.
problem Training difficulties in GANs.
method Explicitly models GANs as a zero-sum game between generator and classifier using mixed strategies, defines resource-bounded best responses and Nash Equilibrium.
result Solves GANGs with RB-NE, demonstrating better performance than standard GANs.
Paper models game theory for defending against data poisoning attacks.
problem Defending against data poisoning attacks using game theory.
method Modeling attacker-defender game, proving non-existence of pure Nash Equilibrium, proposing mixed strategy approach, and developing an algorithm to approximate Nash Equilibrium.
result Demonstrated effectiveness of mixed strategy defense in experiments.
Paper explores limits and possibilities of aligning LLMs with human preferences.
problem Aligning LLMs with diverse human preferences to ensure fairness and informed outcomes.
method Analysis of probabilistic representation of human preferences and preservation of diverse preferences.
result LLMs can't fully align with human preferences using reward-based approaches due to Condorcet cycles, but mixed strategies are statistically possible.
A decision-theoretic bootstrapping method for robust uncertainty quantification.
problem Uncertainty in finite data sets and distributional shift between training and testing data.
method Partition data, train models, sample UQ subsets, define adversarial game, identify optimal mixed strategies.
result Optimal model mixtures and UQ estimates for robust uncertainty quantification.
Study on hypothesis testing games with adversarial classification, showing convergence rates.
problem Adversarial classification in hypothesis testing.
method Mixed strategy Nash equilibria analysis, concentration phenomena examination.
result Exponential rates of convergence of classification errors at equilibrium.
New algorithm finds mixed Nash equilibria in GANs.
problem No provably convergent algorithm exists for general GANs.
method Developed a novel algorithmic framework via an infinite-dimensional two-player game.
result Proved rigorous convergence rates to the mixed Nash Equilibrium.
We argue that the existing regret matchings for Nash equilibrium approximation conduct "jumpy" strategy updating when the probabilities of future plays are set to be proportional to positive regret measures. We propose a geometrical regret matching which features "smooth" strategy updating. Our approach is simple, intu…
In this paper we extend the series of our studies on the properties of an interacting particle model for market microstructure. In our earlier work we defined a Markov process on the majority opinion of the agents, obtained the transition probabilities and analyzed the martingale properties of the ensuing wealth proces…
Exact simulation method for market impact estimation under various execution strategies.
problem Estimating market impact from observed price trajectories under different execution strategies.
method Conditional simulation of point processes under perturbed intensities.
result Exact, event-driven algorithm for reconstructing counterfactual paths.
Optimal adversarial noise algorithms for multiple classifiers using game theory.
problem Designing robust attacks against multiple classifiers.
method Formulating the problem as a two-player, zero-sum game and using Multiplicative Weights Update framework with best response oracles.
result Demonstrated the effectiveness of randomization in adversarial attacks and optimal mixed strategies.
We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of Glosten-Milgrom equilibrium and its as…
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.
This paper improves GANs by ensuring local equilibria are also Nash equilibria, leading to better solutions.
problem Current GAN training methods often converge to local Nash equilibria, which may not be optimal.
method Formalizes GANs as finite games in mixed strategies, ensuring every local equilibrium is a Nash equilibrium.
result The proposed method converges to a resource-bounded Nash equilibrium, producing solutions closer to theoretical predictions.
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…
A novel online learning approach improves stability and performance of GANs.
problem Training GANs is difficult due to instabilities in a minimax optimization problem.
method Viewing GAN training as a zero-sum game, proposing Chekhov GAN, and using online learning strategies.
result Our method provably converges to an equilibrium for semi-shallow GAN architectures and improves stability and performance in practical applications.
Framework for games with uncertain parameters, ensuring no player can improve by changing strategy.
problem Non-cooperative games with globally uncertain parameters and no common prior.
method Mixed strategies and subjective priors, Extended Equilibrium defined by fixed-point argument.
result Existence of Extended Equilibrium under certain conditions.
Paper solves a complex stopping problem using regularization and HJB equations.
problem Time-inconsistent mean-variance optimal stopping problem
method Vanishing regularization method to derive HJB equations and prove existence of solutions
result Formally recovers variational inequalities for original problem
Method identifies mixed Nash equilibria in high dimensions for training mixtures of GANs.
problem Finding Nash equilibria in two-player zero-sum continuous games, especially in high dimensions.
method Parametrizing mixed strategies as mixtures of particles, updating their positions and weights using gradient descent-ascent.
result Global convergence to an approximate equilibrium for the related Langevin gradient-ascent dynamic.
New games model strategic interactions in incomplete information settings.
problem Modeling strategic interactions in incomplete information settings.
method Introduced new games that map input to private player types, aggregate strategies, and converge to near-Nash equilibria.
result Games can recover meaningful strategic interactions from real data.
The paper explores game-theoretic alignment of LLMs with human preferences, finding limitations and conditions.
problem Aligning LLMs with human preferences using game theory.
method Systematic study of payoff choices in a two-player zero-sum game for desirable alignment properties.
result Impossibility of preference matching in game-theoretic LLM alignment under standard assumptions.
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.
SelectMix improves deep learning robustness against noisy labels.
problem Deep neural networks memorize noisy labels, degrading performance.
method Confidence-guided targeted sample mixing with soft labels.
result SelectMix consistently outperforms baseline methods on noisy label datasets.
Unified framework for decentralized bilevel optimization with various heterogeneity-correction strategies.
problem Decentralized bilevel optimization with neighborhood communications and data heterogeneity.
method SPARKLE: Single-loop Primal-dual Algorithm for decentralized bilevel optimization, incorporating various heterogeneity-correction techniques.
result Unified convergence analysis for SPARKLE with state-of-the-art convergence rates compared to existing algorithms.
In this paper, we present a multi-period trading model in the style of Kyle (1985)'s inside trading model, by assuming that there are at least two insiders in the market with long-lived private information, under the requirement that each insider publicly discloses his stock trades after the fact. Based on this model, …
Two new RL methods enable deep learning of MFG equilibria.
problem Efficiently learning equilibria in Mean Field Games using RL.
method Two novel RL methods: distillation and online mixing.
result Deep RL algorithms can now solve various MFGs.
Method generates i.i.d. samples from GT data using space-time mixing.
problem Generating synthetic i.i.d. samples from high-dimensional real-valued distributions.
method Space-time mixing strategies, diffusion bridges, and score-matching.
result Optimal transport from initial to target distribution.
Study of 2imes2 zero-sum games with noisy observations and commitments.
problem Analyzing 2imes2 zero-sum games with noisy observations and commitments. method Modeling a 2imes2 zero-sum game with a leader committing to a strategy and a follower observing a noisy version of the leader's action. result Observing the leader's action is either beneficial or immaterial for the follower, and the equilibrium payoff is bounded.
New Bayesian method improves Pareto front estimation in multitask finetuning.
problem Efficiently estimating Pareto fronts for multitask finetuning.
method Variational Model Merging using non-Gaussian posteriors.
result More flexible posteriors lead to better Pareto front estimates.
Paper studies convergence of Mean-Field GDA dynamics for MNE of continuous games.
problem Finding mixed Nash equilibria in continuous games.
method Two-scale Mean-Field Gradient Descent Ascent dynamics.
result Two-scale Mean-Field GDA converges exponentially to MNE without convexity assumptions.
New discrete-time model shows insider trading dynamics.
problem Modeling insider trading with discrete time and noise traders.
method Formulated as a game with three types of traders, including an insider, noise traders, and a market maker. Proved existence of sequential Kyle equilibrium for various distributions and information flows.
result Equilibria exist in mixed strategies but not in pure strategies, unlike in Kyle's original model.
A new method improves network modeling by mixing multiple models.
problem Learning network connections from noisy data.
method Mixing multiple models to improve individual model performances.
result The method outperforms existing approaches even when models are misspecified.
We introduce a scalable measure of curvature for analyzing training dynamics of large language models.
problem Analyzing the training dynamics of large language models due to high computational cost of measuring Hessian sharpness.
method We introduce critical sharpness and relative critical sharpness as computationally efficient measures capturing Hessian sharpness phenomena.
result We provide the first demonstration of sharpness phenomena at scale up to 7B parameters.
Randomization is minimax-optimal for variance in experimental design, even with structure.
problem Designing optimal randomized experiments for variance minimization.
method Analyzing permutation symmetric and non-symmetric sets of outcomes, proposing inference-constrained MSOD.
result Randomization is minimax-optimal for variance, even with structure, and requires uniformity constraints for Fisher's exact test.
We introduce a near-linear complexity (geometric and meshless/algebraic) multigrid/multiresolution method for PDEs with rough (L∞) coefficients with rigorous a-priori accuracy and performance estimates. The method is discovered through a decision/game theory formulation of the problems of (1) identifying restri…
The study uses Hidden Markov Models to analyze student enrollment patterns and academic performance.
problem Limited understanding of how enrollment patterns affect academic performance.
method Applied Hidden Markov Models to categorize enrollment strategies and compare academic outcomes.
result Mixed enrollment strategies lead to better academic performance, especially during part-time semesters.