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Found 64 papers, 8 papers with code
Tractable Local Equilibria in Non-Concave Games
While Online Gradient Descent and other no-regret learning procedures are known to efficiently converge to coarse correlated equilibrium in games where each agent's utility is concave in their own strategy, this is not the case when the utilities are non-concave, a situation that is common in machine learning applications where the agents' strategies are parameterized by deep neural networks, or the agents' utilities are computed by a neural network, or both.
From External to Swap Regret 2.0: An Efficient Reduction and Oblivious Adversary for Large Action Spaces
We provide a novel reduction from swap-regret minimization to external-regret minimization, which improves upon the classical reductions of Blum-Mansour [BM07] and Stolz-Lugosi [SL05] in that it does not require finiteness of the space of actions.
Smooth Nash Equilibria: Algorithms and Complexity
We show that both weak and strong $\sigma$-smooth Nash equilibria have superior computational properties to Nash equilibria: when $\sigma$ as well as an approximation parameter $\epsilon$ and the number of players are all constants, there is a constant-time randomized algorithm to find a weak $\epsilon$-approximate $\sigma$-smooth Nash equilibrium in normal-form games.
Online Learning and Solving Infinite Games with an ERM Oracle
In this setting, we provide learning algorithms that only rely on best response oracles and converge to approximate-minimax equilibria in two-player zero-sum games and approximate coarse correlated equilibria in multi-player general-sum games, as long as the game has a bounded fat-threshold dimension.
SDYN-GANs: Adversarial Learning Methods for Multistep Generative Models for General Order Stochastic Dynamics
We introduce adversarial learning methods for data-driven generative modeling of the dynamics of $n^{th}$-order stochastic systems.
Learning and Testing Latent-Tree Ising Models Efficiently
We provide time- and sample-efficient algorithms for learning and testing latent-tree Ising models, i. e. Ising models that may only be observed at their leaf nodes.
EM's Convergence in Gaussian Latent Tree Models
Our results for the landscape of the log-likelihood function in general latent tree models provide support for the extensive practical use of maximum likelihood based-methods in this setting.
STay-ON-the-Ridge: Guaranteed Convergence to Local Minimax Equilibrium in Nonconvex-Nonconcave Games
In particular, our method is not designed to decrease some potential function, such as the distance of its iterate from the set of local min-max equilibria or the projected gradient of the objective, but is designed to satisfy a topological property that guarantees the avoidance of cycles and implies its convergence.
Efficient Truncated Linear Regression with Unknown Noise Variance
In this paper, we provide the first computationally and statistically efficient estimators for truncated linear regression when the noise variance is unknown, estimating both the linear model and the variance of the noise.
Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problems
In practice, to allow for increased expressivity, we propose to do posterior sampling in the latent space of a pre-trained generative model.
What Makes A Good Fisherman? Linear Regression under Self-Selection Bias
In known-index self-selection, the identity of the observed model output is observable; in unknown-index self-selection, it is not.
Estimation of Standard Auction Models
We provide efficient estimation methods for first- and second-price auctions under independent (asymmetric) private values and partial observability.
The Complexity of Markov Equilibrium in Stochastic Games
Previous work for learning Markov CCE policies all required exponential time and sample complexity in the number of players.
Multi-agent Reinforcement Learning
reinforcement-learning
+1
How Good are Low-Rank Approximations in Gaussian Process Regression?
In particular, we bound the Kullback-Leibler divergence between an exact GP and one resulting from one of the afore-described low-rank approximations to its kernel, as well as between their corresponding predictive densities, and we also bound the error between predictive mean vectors and between predictive covariance matrices computed using the exact versus using the approximate GP.
Fast Rates for Nonparametric Online Learning: From Realizability to Learning in Games
Our contributions are two-fold: - In the realizable setting of nonparametric online regression with the absolute loss, we propose a randomized proper learning algorithm which gets a near-optimal cumulative loss in terms of the sequential fat-shattering dimension of the hypothesis class.
Near-Optimal No-Regret Learning for Correlated Equilibria in Multi-Player General-Sum Games
Recently, Daskalakis, Fishelson, and Golowich (DFG) (NeurIPS`21) showed that if all agents in a multi-player general-sum normal-form game employ Optimistic Multiplicative Weights Update (OMWU), the external regret of every player is $O(\textrm{polylog}(T))$ after $T$ repetitions of the game.
Recommender Systems meet Mechanism Design
We propose a mechanism design framework for this setting, building on a recent robustification framework by Brustle et al., which disentangles the statistical challenge of estimating a multi-dimensional prior from the task of designing a good mechanism for it, and robustifies the performance of the latter against the estimation error of the former.
Near-Optimal No-Regret Learning in General Games
We show that Optimistic Hedge -- a common variant of multiplicative-weights-updates with recency bias -- attains ${\rm poly}(\log T)$ regret in multi-player general-sum games.
Statistical Estimation from Dependent Data
We consider a general statistical estimation problem wherein binary labels across different observations are not independent conditioned on their feature vectors, but dependent, capturing settings where e. g. these observations are collected on a spatial domain, a temporal domain, or a social network, which induce dependencies.
Independent Policy Gradient Methods for Competitive Reinforcement Learning
We obtain global, non-asymptotic convergence guarantees for independent learning algorithms in competitive reinforcement learning settings with two agents (i. e., zero-sum stochastic games).
Efficient Methods for Structured Nonconvex-Nonconcave Min-Max Optimization
The use of min-max optimization in adversarial training of deep neural network classifiers and training of generative adversarial networks has motivated the study of nonconvex-nonconcave optimization objectives, which frequently arise in these applications.
Sample-Optimal and Efficient Learning of Tree Ising models
We show that $n$-variable tree-structured Ising models can be learned computationally-efficiently to within total variation distance $\epsilon$ from an optimal $O(n \ln n/\epsilon^2)$ samples, where $O(\cdot)$ hides an absolute constant which, importantly, does not depend on the model being learned - neither its tree nor the magnitude of its edge strengths, on which we place no assumptions.
Tight last-iterate convergence rates for no-regret learning in multi-player games
We also show that the $O(1/\sqrt{T})$ rate is tight for all $p$-SCLI algorithms, which includes OG as a special case.
Computationally and Statistically Efficient Truncated Regression
We provide a computationally and statistically efficient estimator for the classical problem of truncated linear regression, where the dependent variable $y = w^T x + \epsilon$ and its corresponding vector of covariates $x \in R^k$ are only revealed if the dependent variable falls in some subset $S \subseteq R$; otherwise the existence of the pair $(x, y)$ is hidden.
The Complexity of Constrained Min-Max Optimization
In this paper, we provide a characterization of the computational complexity of the problem, as well as of the limitations of first-order methods in constrained min-max optimization problems with nonconvex-nonconcave objectives and linear constraints.
Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models
Particle coordinates at a single time instant, possibly noisy or truncated, are recorded in each snapshot but are unpaired across the snapshots.
Truncated Linear Regression in High Dimensions
As a corollary, our guarantees imply a computationally efficient and information-theoretically optimal algorithm for compressed sensing with truncation, which may arise from measurement saturation effects.
Constant-Expansion Suffices for Compressed Sensing with Generative Priors
Using this theorem we can show that a matrix concentration inequality known as the Weight Distribution Condition (WDC), which was previously only known to hold for Gaussian matrices with logarithmic aspect ratio, in fact holds for constant aspect ratios too.
Learning Ising models from one or multiple samples
As corollaries of our main theorem, we derive bounds when the model's interaction matrix is a (sparse) linear combination of known matrices, or it belongs to a finite set, or to a high-dimensional manifold.
How Good are Low-Rank Approximations in Gaussian Process Regression?
In particular, we bound the Kullback-Leibler divergence between an exact GP and one resulting from one of the afore-described low-rank approximations to its kernel, as well as between their corresponding predictive densities, and we also bound the error between predictive mean vectors and between predictive covariance matrices computed using the exact versus using the approximate GP.
Logistic-Regression with peer-group effects via inference in higher order Ising models
In this work we study extensions of these to models with higher-order sufficient statistics, modeling behavior on a social network with peer-group effects.
GANs with Conditional Independence Graphs: On Subadditivity of Probability Divergences
GANs, however, are designed in a model-free fashion where no additional information about the underlying distribution is available.
Last Iterate is Slower than Averaged Iterate in Smooth Convex-Concave Saddle Point Problems
In this paper we study the smooth convex-concave saddle point problem.
Multi-Item Mechanisms without Item-Independence: Learnability via Robustness
When item values are sampled from more general graphical models, we combine our robustness theorem with novel sample complexity results for learning Markov Random Fields or Bayesian Networks in Prokhorov distance, which may be of independent interest.
SGD Learns One-Layer Networks in WGANs
Generative adversarial networks (GANs) are a widely used framework for learning generative models.
Learning from weakly dependent data under Dobrushin's condition
Indeed, we show that the standard complexity measures of Gaussian and Rademacher complexities and VC dimension are sufficient measures of complexity for the purposes of bounding the generalization error and learning rates of hypothesis classes in our setting.
Regression from Dependent Observations
The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates.
HOGWILD!-Gibbs can be PanAccurate
Hence, the expectation of any function that is Lipschitz with respect to a power of the Hamming distance, can be estimated with a bias that grows logarithmically in $n$.
Smoothed Analysis of Discrete Tensor Decomposition and Assemblies of Neurons
We give an application to recovering assemblies of neurons.
Efficient Statistics, in High Dimensions, from Truncated Samples
We provide an efficient algorithm for the classical problem, going back to Galton, Pearson, and Fisher, of estimating, with arbitrary accuracy the parameters of a multivariate normal distribution from truncated samples.
Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization
Motivated by applications in Game Theory, Optimization, and Generative Adversarial Networks, recent work of Daskalakis et al \cite{DISZ17} and follow-up work of Liang and Stokes \cite{LiangS18} have established that a variant of the widely used Gradient Descent/Ascent procedure, called "Optimistic Gradient Descent/Ascent (OGDA)", exhibits last-iterate convergence to saddle points in {\em unconstrained} convex-concave min-max optimization problems.
The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization
Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study.
Learning and Testing Causal Models with Interventions
We consider testing and learning problems on causal Bayesian networks as defined by Pearl (Pearl, 2009).
The Robust Manifold Defense: Adversarial Training using Generative Models
Our formulation involves solving a min-max problem, where the min player sets the parameters of the classifier and the max player is running our attack, and is thus searching for adversarial examples in the {\em low-dimensional} input space of the spanner.
Training GANs with Optimism
Moreover, we show that optimistic mirror decent addresses the limit cycling problem in training WGANs.
Concentration of Multilinear Functions of the Ising Model with Applications to Network Data
We prove near-tight concentration of measure for polynomial functions of the Ising model under high temperature.
Learning Multi-item Auctions with (or without) Samples
The second is a more general max-min learning setting that we introduce, where we are given "approximate distributions," and we seek to compute an auction whose revenue is approximately optimal simultaneously for all "true distributions" that are close to the given ones.
Priv’IT: Private and Sample Efficient Identity Testing
We develop differentially private hypothesis testing methods for the small sample regime.
Which Distribution Distances are Sublinearly Testable?
Given samples from an unknown distribution $p$ and a description of a distribution $q$, are $p$ and $q$ close or far?
Testing Symmetric Markov Chains from a Single Trajectory
We initiate the study of Markov chain testing, assuming access to a single trajectory of a Markov Chain.
Priv'IT: Private and Sample Efficient Identity Testing
We develop differentially private hypothesis testing methods for the small sample regime.
A Converse to Banach's Fixed Point Theorem and its CLS Completeness
Our first result is a strong converse of Banach's theorem, showing that it is a universal analysis tool for establishing global convergence of iterative methods to unique fixed points, and for bounding their convergence rate.
Square Hellinger Subadditivity for Bayesian Networks and its Applications to Identity Testing
As an application of our inequality, we show that distinguishing whether two Bayesian networks $P$ and $Q$ on the same (but potentially unknown) DAG satisfy $P=Q$ vs $d_{\rm TV}(P, Q)>\epsilon$ can be performed from $\tilde{O}(|\Sigma|^{3/4(d+1)} \cdot n/\epsilon^2)$ samples, where $d$ is the maximum in-degree of the DAG and $\Sigma$ the domain of each variable of the Bayesian networks.
Testing Ising Models
Given samples from an unknown multivariate distribution $p$, is it possible to distinguish whether $p$ is the product of its marginals versus $p$ being far from every product distribution?
Ten Steps of EM Suffice for Mixtures of Two Gaussians
In the finite sample regime, we show that, under a random initialization, $\tilde{O}(d/\epsilon^2)$ samples suffice to compute the unknown vectors to within $\epsilon$ in Mahalanobis distance, where $d$ is the dimension.
A Size-Free CLT for Poisson Multinomials and its Applications
Finally, leveraging the structural properties of the Fourier spectrum of PMDs we show that these distributions can be learned from $O_k(1/\varepsilon^2)$ samples in ${\rm poly}_k(1/\varepsilon)$-time, removing the quasi-polynomial dependence of the running time on $1/\varepsilon$ from the algorithm of Daskalakis, Kamath, and Tzamos.
Learning in Auctions: Regret is Hard, Envy is Easy
Our results for XOS valuations are enabled by a novel Follow-The-Perturbed-Leader algorithm for settings where the number of experts is infinite, and the payoff function of the learner is non-linear.
Optimal Testing for Properties of Distributions
Given samples from an unknown distribution $p$, is it possible to distinguish whether $p$ belongs to some class of distributions $\mathcal{C}$ versus $p$ being far from every distribution in $\mathcal{C}$?
On the Structure, Covering, and Learning of Poisson Multinomial Distributions
We prove a structural characterization of these distributions, showing that, for all $\varepsilon >0$, any $(n, k)$-Poisson multinomial random vector is $\varepsilon$-close, in total variation distance, to the sum of a discretized multidimensional Gaussian and an independent $(\text{poly}(k/\varepsilon), k)$-Poisson multinomial random vector.
Testing Poisson Binomial Distributions
We provide a sample near-optimal algorithm for testing whether a distribution $P$ supported on $\{0,..., n\}$ to which we have sample access is a Poisson Binomial distribution, or far from all Poisson Binomial distributions.
Optimum Statistical Estimation with Strategic Data Sources
We propose an optimum mechanism for providing monetary incentives to the data sources of a statistical estimator such as linear regression, so that high quality data is provided at low cost, in the sense that the sum of payments and estimation error is minimized.
Faster and Sample Near-Optimal Algorithms for Proper Learning Mixtures of Gaussians
The algorithm requires ${O}(\log{N}/\varepsilon^2)$ samples from the unknown distribution and ${O}(N \log N/\varepsilon^2)$ time, which improves previous such results (such as the Scheff\'e estimator) from a quadratic dependence of the running time on $N$ to quasilinear.
Learning $k$-Modal Distributions via Testing
The learning algorithm is given access to independent samples drawn from an unknown $k$-modal distribution $p$, and it must output a hypothesis distribution $\widehat{p}$ such that with high probability the total variation distance between $p$ and $\widehat{p}$ is at most $\epsilon.$ Our main goal is to obtain \emph{computationally efficient} algorithms for this problem that use (close to) an information-theoretically optimal number of samples.
Learning Poisson Binomial Distributions
Our second main result is a {\em proper} learning algorithm that learns to $\eps$-accuracy using $\tilde{O}(1/\eps^2)$ samples, and runs in time $(1/\eps)^{\poly (\log (1/\eps))} \cdot \log n$.
