New method improves convergence for smooth games.
problem Improving convergence for smooth games.
method Stochastic Hamiltonian Gradient Methods (SHGD).
result SHGD converges linearly to the neighbourhood of a stationary point.
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48 results for “Bilinear Games”
New algorithm reduces regret in graphical bilinear bandits.
problem Optimizing decisions in a network of agents playing bilinear games.
method Optimism in the face of uncertainty principle applied to combinatorial NP-hard problem.
result Upper bound of on -regret demonstrated.
Improved SEG method converges to Nash equilibrium in bilinear games.
problem Stochastic bilinear minimax optimization problem
method Stochastic ExtraGradient (SEG) method with constant step size, iteration averaging, and scheduled restarting.
result Provable convergence to Nash equilibrium under standard settings, optimal convergence rate in interpolation setting.
We consider differentiable games where the goal is to find a Nash equilibrium. The machine learning community has recently started using variants of the gradient method (GD). Prime examples are extragradient (EG), the optimistic gradient method (OG) and consensus optimization (CO), which enjoy linear convergence in cas…
The extragradient method accelerates convergence in complex game dynamics.
problem Complex interactions in game dynamics cause simple methods to diverge, necessitating more sophisticated approaches.
method A polynomial-based analysis to identify three scenarios for accelerated convergence of the momentum extragradient method.
result The momentum extragradient method achieves faster convergence under specific eigenvalue conditions.
We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function whose output is being applied to a bilinear zero-sum game. This class of games is motivated by the indirect nature of the competition in Ge…
Improved convergence rates for saddle-point optimization algorithms.
problem Understanding last-iterate convergence rates for saddle-point optimization algorithms in constrained settings.
method Expanding the understanding of last-iterate convergence for Optimistic Gradient Descent Ascent (OGDA) and Optimistic Multiplicative Weights Update (OMWU) in the constrained setting.
result Linear last-iterate convergence achieved with a universal constant learning rate for OMWU in bilinear games over the simplex.
Min-max formulations have attracted great attention in the ML community due to the rise of deep generative models and adversarial methods, while understanding the dynamics of gradient algorithms for solving such formulations has remained a grand challenge. As a first step, we restrict to bilinear zero-sum games and giv…
Improves training GANs by escaping limit cycles.
problem Limit cycling behavior in training GANs.
method Predictive Centripetal Acceleration Algorithm (PCAA) combined with Adam.
result PCAA improves convergence rates and effectively trains GANs.
New method accelerates smooth games using spectral shape analysis.
problem Accelerating optimization in smooth games with complex numerical challenges.
method Matrix iteration theory and spectral shape analysis to characterize and manipulate acceleration.
result Identified a continuum of optimization strategies from convex minimization to gradient descent.
Proposes CoPO, a new policy optimization method for competitive games.
problem Designing efficient optimization methods for competitive Markov decision processes.
method Competitive policy optimization (CoPO) approach that exploits game-theoretic nature of competitive games.
result Stable optimization, convergence to sophisticated strategies, and higher scores compared to baseline methods.
Transforms game optimization dynamics into frequency domain for precise hyperparameter analysis.
problem Analyzing convergence of hyperparameters in game optimization.
method Frequency-domain framework using High-Resolution Differential Equations (HRDEs) and Laplace transforms.
result Derives precise convergence criteria for the Lookahead algorithm.
Negative momentum accelerates convergence in minimax games but at a suboptimal rate.
problem The convergence rate of negative momentum in minimax games is suboptimal.
method Extending variational inequality formulation, connecting momentum method with Chebyshev polynomials.
result Negative momentum accelerates convergence locally but at a suboptimal rate.
Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradient-based Nikaido-Isoda (GNI) function which serves: (i) as a merit function, vani…
New framework recovers reward and rationality parameters from game behavior.
problem Statistical ambiguity in identifying reward and rationality parameters in competitive games.
method Blind Inverse Game Theory (Blind-IGT) using entropy-regularized Quantal Response Equilibrium and Normalized Least Squares (NLS) estimator.
result Optimal convergence rate of for joint parameter recovery.
This work finds mixed equilibria in machine learning problems using measures and simultaneous gradient ascent-descent.
problem Finding pure equilibria in machine learning problems is computationally hard.
method Entropic regularization, simultaneous gradient ascent-descent, and particle discretization in the Wasserstein metric.
result Global convergence towards the global equilibrium in mixed equilibria problems.
Last-Iterate Convergence of Saddle-Point Optimizers via High-Resolution Differential Equationsmath.OC
New ODE models show saddle-point optimization methods converge differently, with last-iterate convergence for OGDA.
problem Analyzing convergence properties of saddle-point optimization methods.
method High-Resolution Differential Equations (HRDEs) to design differential equation models for saddle-point optimization methods.
result HRDEs reveal last-iterate convergence for Optimistic Gradient Descent Ascent (OGDA) in bilinear games.
OMWU shows last iterate convergence in convex-concave games.
problem Optimizing in constrained min-max optimization landscapes.
method OMWU (Optimistic Multiplicative-Weights Update) in the no-regret online learning framework.
result OMWU exhibits last iterate convergence for convex-concave games, generalizing previous results.
We examine two different techniques for parameter averaging in GAN training. Moving Average (MA) computes the time-average of parameters, whereas Exponential Moving Average (EMA) computes an exponentially discounted sum. Whilst MA is known to lead to convergence in bilinear settings, we provide the -- to our knowledge …
Training generative adversarial networks (GANs) often suffers from cyclic behaviors of iterates. Based on a simple intuition that the direction of centripetal acceleration of an object moving in uniform circular motion is toward the center of the circle, we present the Simultaneous Centripetal Acceleration (SCA) method…
This paper presents a novel unifying framework of bilinear LSTMs that can represent and utilize the nonlinear interaction of the input features present in sequence datasets for achieving superior performance over a linear LSTM and yet not incur more parameters to be learned. To realize this, our unifying framework allo…
Generalization of twistor spinors to Kähler manifolds which are called Kählerian twistor spinors are considered. We find the differential equation satisfied by the bilinear forms of Kählerian twistor spinors. We show that the bilinear form equation reduces to Kählerian conformal Killing-Yano equation under special cond…
Algorithm identifies correct hypothesis from alternatives in bandit problems.
problem Efficiently identifying the correct hypothesis from a finite set of alternatives in structured stochastic multi-armed bandits.
method Frank-Wolfe Self-Play (FWSP) reformulates the game as a saddle-point problem, using a differential-inclusion argument to prove convergence.
result Convergence of the game value for best-arm identification in linear bandits, with uniform global convergence to the optimal value.
Owing to their connection with generative adversarial networks (GANs), saddle-point problems have recently attracted considerable interest in machine learning and beyond. By necessity, most theoretical guarantees revolve around convex-concave (or even linear) problems; however, making theoretical inroads towards effici…
Algorithm identifies bilinear dynamical systems from noisy data.
problem Learning a realization of a partially observed bilinear dynamical system.
method Regression of outputs to highly correlated covariates for Markov-like parameters.
result High probability error bounds on identification algorithm under uniform stability assumption.
In this paper, we extend Su-Zhang's Cheeger-Mueller type theorem for symmetric bilinear torsions to manifolds with boundary in the case that the Riemannian metric and the non-degenerate symmetric bilinear form are of product structure near the boundary. Our result also extends Bruening-Ma's Cheeger-Mueller type theorem…
Bilinear MLPs offer a new way to interpret deep learning models without complex nonlinearities.
problem Lack of mechanistic understanding in how MLPs compute.
method Introduced bilinear MLPs without element-wise nonlinearities, analyzed their weights using tensor and eigendecomposition.
result Bilinear MLPs provide interpretable weight structures and enable adversarial attacks and overfitting analysis.
Identifies bilinear systems from a single trajectory with optimal sample complexity.
problem Learning bilinear systems from a single trajectory of states and inputs.
method Uses a mild marginal mean-square stability assumption and martingale small-ball condition.
result Sample complexity and statistical error rates are optimal.
Bernhard Riemann 1861 revisited: existence of flat coordinates for an arbitrary bilinear formmath.DG
Generalizes Riemann's results on flat coordinates for non-symmetric bilinear forms.
problem Finding flat coordinates for non-symmetric bilinear forms.
method Provides explicit necessary and sufficient conditions for a tensor field of type (0,2) to be flat.
result Explicit conditions for a tensor field to have constant entries in local coordinates.
The theory of harmonic symmetric bilinear forms on a Riemannian manifold is an analogue of the theory of harmonic exterior differential forms on this manifold. To show this, we must consider every symmetric bilinear form on a Riemannian manifold as a one-form with values in the cotangent bundle of this manifold. In thi…
Paper reduces sample complexity for bilinear systems identification to nearly constant.
problem Identifying discrete-time bilinear systems under bounded disturbances.
method Uses trajectory-dependent regressors and polynomial mean-square state growth analysis.
result Proves sample complexity of for estimation error .
This note provides a neat and enjoyable expansion and application of the magnificent Ordentlich-Cover theory of "universal portfolios." I generalize Cover's benchmark of the best constant-rebalanced portfolio (or 1-linear trading strategy) in hindsight by considering the best bilinear trading strategy determined in hin…
Enhances knot invariants using bilinear forms on vector spaces.
problem Improving classical and virtual knot invariants.
method Uses bilinear forms on vector spaces indexed by pairs of elements of a finite quandle.
result New enhanced invariants of knots and links.
Constructs a bilinear form from a quasimorphism on symplectic manifold groups.
problem Understanding symplectic group properties through quasimorphisms and bilinear forms.
method Develops machinery to construct a real-valued bilinear form from a quasimorphism on the commutator subgroup of symplectic group.
result The constructed bilinear form controls extendability of quasimorphisms and triviality of characteristic classes.
Generalized Bilinear Deep Convolutional Neural Networks for Multimodal Biometric Identificationcs.LG
In this paper, we propose to employ a bank of modality-dedicated Convolutional Neural Networks (CNNs), fuse, train, and optimize them together for person classification tasks. A modality-dedicated CNN is used for each modality to extract modality-specific features. We demonstrate that, rather than spatial fusion at the…
On bilinear biquandlesmath.QA
We define a type of biquandle which is a generalization of symplectic quandles. We use the extra structure of these bilinear biquandles to define new knot and link invariants and give some examples.
Generalized B-Opersmath.AG
Introduces and studies generalized B-opers with bilinear forms.
problem Understanding higher rank opers with bilinear forms.
method Studies the structure of generalized B-opers using jet bundles and geometric structures on Riemann surfaces.
result Structure of generalized B-opers is studied and related to jet bundles and geometric structures.
A parsimonious model reduces over-parameterization in skewed matrix variate mixtures.
problem Over-parameterization in skewed matrix variate mixtures.
method Parsimonious family of 256 models using bilinear factor analyzers constrained over clusters, with AECM algorithm for estimation.
result Extensive simulations and real-world datasets (MNIST, Olivetti faces) demonstrate the method's effectiveness.
Study learns linear system dynamics from noisy bilinear data.
problem Learning linear dynamics from bilinear observations with process and measurement noise.
method Regression with Kronecker product design, data-dependent and independent error bounds.
result Upper bounds on statistical error rates and sample complexity for learning dynamics matrices.
We use the Jones-Wenzl idempotents to construct a basis of Temperley-Lieb algebra TL_n. This allows a short calculation for a Gram determinant of Lickorish's bilinear form on the Temperley-Lieb algebra.
Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.
problem Optimal control from bilinear observations in linear systems is challenging.
method Analytical and numerical methods to study the non-convex cost-to-go and non-affine optimal controllers.
result The Separation Principle does not hold for bilinear observations, leading to non-convex costs and non-affine optimal controllers.
This thesis is concerned with the theory of invariant bilinear differential pairings on parabolic geometries. It introduces the concept formally with the help of the jet bundle formalism and provides a detailed analysis. More precisely, after introducing the most important notations and definitions, we first of all giv…
Unified bounds for sketched bilinear forms in machine learning and statistics.
problem Uniform bounds on sketched bilinear forms for modern analyses.
method Generic chaining and new techniques for handling suprema over pairs of sets.
result Improved convergence bounds for sketched Federated Learning and bandit algorithms.
BiN normalizes financial time-series for better forecasting.
problem Non-stationarity and multimodality in financial time-series data.
method Bilinear Normalization (BiN) incorporated into TABL networks.
result BiN-TABL outperforms other normalization methods in financial forecasting.
Proposes a low-rank bilinear pooling model for link prediction in knowledge graphs.
problem Link prediction in incomplete knowledge graphs.
method Factorized bilinear pooling model with Tucker decomposition constraints.
result Efficient and parameter-efficient model with low-rank approximation.
Study dynamics of alternating minimization for bilinear regression under large system limits.
problem Understanding the time evolution of alternating minimization for bilinear regression.
method Replica method applied to a multi-temperature glassy system.
result Dynamics of alternating minimization can be described by a two-dimensional discrete stochastic process.
Novel hybrid bilinear model improves epilepsy diagnosis accuracy.
problem Improving accuracy in epilepsy diagnosis and treatment.
method Hybrid bilinear deep learning network using sEEG and audiovisual monitoring.
result Obtained F1-scores of 97.4% and 97.2% on two seizure datasets.
Vector-valued neural learning has emerged as a promising direction in deep learning recently. Traditionally, training data for neural networks (NNs) are formulated as a vector of scalars; however, its performance may not be optimal since associations among adjacent scalars are not modeled. In this paper, we propose a n…