The paper examines Nash equilibrium in GANs for stationary Gaussian processes.
problem Existence and uniqueness of Nash equilibrium in GANs for stationary Gaussian processes.
method Analyzes the existence of Nash equilibrium in GANs for stationary Gaussian processes, considering different discriminator families.
result The existence of Nash equilibrium depends on the discriminator family and symmetry properties of the generator family.
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.
Study on local convergence of min-max algorithms to differential equilibria on Riemannian manifolds.
problem Solving zero-sum differential games on Riemannian manifolds.
method Analysis of two simultaneous min-max algorithms, τ-GDA and τ-SGA, to differential Stackelberg and Nash equilibria, with conditions for linear convergence and asymptotic approximation. result Established sufficient conditions for linear convergence of τ-GDA and demonstrated faster convergence of τ-SGA in some cases. MpFL models clients as strategic players to reach equilibrium with less communication.
problem Real-world clients act independently with individual objectives, not aligned with a shared global model.
method MpFL uses game-theoretic modeling and PEARL-SGD algorithm for local updates and communication.
result PEARL-SGD reaches an equilibrium with less communication than non-local updates in stochastic setup.
A new method relaxes molecules without needing non-equilibrium data.
problem Molecular relaxation requires understanding non-equilibrium structures.
method MoreRed: molecular relaxation by reverse diffusion with time step prediction.
result MoreRed learns a simpler pseudo potential energy surface.
We develop a model for the evolution of wealth in a non-conservative economic environment, extending a theory developed earlier by the authors. The model considers a system of rational agents interacting in a game theoretical framework. This evolution drives the dynamic of the agents in both wealth and economic configu…
Alternative finance models from physics for non-equilibrium systems.
problem Inequities of classical finance models in physics-based perspective.
method Physics-based insights for non-equilibrium finance models.
result Alternative models for non-equilibrium finance systems.
Neural network models colloidal particle dynamics in non-equilibrium systems.
problem Analyzing non-equilibrium dynamics of many-body colloidal systems.
method Combining power functional theory and machine learning, training a neural network to predict internal force fields.
result The neural network accurately predicts dynamics in non-equilibrium systems, in good agreement with simulations.
TTUR improves GAN training, converging to local Nash equilibrium.
problem Proving convergence of GAN training.
method Two time-scale update rule (TTUR) with stochastic gradient descent.
result TTUR converges to a local Nash equilibrium under mild assumptions.
In an earlier work we identified the types and numbers of static equilibrium points of solids arising from fine, equidistant n-discretrizations of smooth, convex surfaces. We showed that such discretizations carry equilibrium points on two scales: the local scale corresponds to the discretization, the global scale to…
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general assumptions on the cost function. This evolution drives the dynamic of the agents i…
EP learns like BPTT but with local weight updates.
problem Existing EP lacks a local time learning rule.
method C-EP updates weights simultaneously with neuron dynamics.
result C-EP follows BPTT gradients and performs well.
Proposes a new algorithm to find local Nash equilibria in zero-sum games.
problem Cannot guarantee convergence to local Nash equilibria with previous methods.
method Local symplectic surgery, a two-timescale procedure.
result Local Nash equilibria are the only attracting fixed points.
GANs may not have Nash equilibria, but proximal training can find solutions.
problem Existence of Nash equilibria in GANs optimization.
method Proximal training approach to find solutions.
result Proximal training finds solutions to GAN problems.
Paper analyzes adversarial attacks and defenses using game theory.
problem Unclear conditions for optimal attacks and defenses in adversarial learning.
method Game-theoretic framework with locally linear decision boundary model.
result Fast Gradient Method attack and Randomized Smoothing defense form a Nash Equilibrium.
Despite the growing prominence of generative adversarial networks (GANs), optimization in GANs is still a poorly understood topic. In this paper, we analyze the "gradient descent" form of GAN optimization i.e., the natural setting where we simultaneously take small gradient steps in both generator and discriminator par…
We consider a simple model of a closed economic system where the total money is conserved and the number of economic agents is fixed. In analogy to statistical systems in equilibrium, money and the average money per economic agent are equivalent to energy and temperature, respectively. We investigate the effect of the …
Proposes an efficient alternative to nonconvex-nonconcave min-max optimization.
problem Min-max optimization challenges in nonconvex-nonconcave settings.
method Introduces ε-greedy adversarial equilibrium model and proves its existence.
result Existence of ε-greedy adversarial equilibrium for smooth bounded functions.
A decentralized approach for agents to learn and optimize collectively.
problem Challenges in coordinating non-cooperative agents to solve complex sequential decision problems.
method Designing a learning environment where agents learn by trading and optimizing local objectives, leading to a Nash equilibrium.
result Decentralized reinforcement learning algorithms that can handle various decision-making scenarios.
Unified approach to time-inconsistent problems with distribution-dependent rewards.
problem Time-inconsistent problems with distribution-dependent rewards in behavioral finance and economics.
method Equilibrium master equation on Wasserstein space, refined derivatives, Itô's formula.
result Unified approach to find equilibrium solutions for time-inconsistent problems.
EP algorithm improved for CNNs and real-time learning.
problem EP's long simulation times and non-local learning rule limitations.
method Discrete-time formulation, continual weight updates, local time information.
result C-EP achieves best performance on MNIST with CNNs.
Paper tackles inverse reinforcement learning with non-optimal demonstrations in zero-sum games.
problem Inverse reinforcement learning with sub-optimal expert demonstrations in zero-sum games.
method Introduces a new objective function and algorithm to find reward function and strategies without decoupling agents.
result Demonstrates recovery of reward functions and strategies with good quality from sub-optimal expert demonstrations.
Study on liquid-vapor interfaces in stable equilibrium without assuming prior regularity.
problem Understanding the conditions for a liquid-vapor interface to be in stable equilibrium without assuming prior regularity.
method Proposes a weakest set of mathematical assumptions using varifold regularity theory and identifies a suitable stability condition.
result The liquid-vapor interface is a smoothly embedded analytic surface in stable equilibrium.
Common perpendiculars equidistribute in negatively curved spaces.
problem Equidistribution of common perpendiculars in negatively curved spaces.
method Analyzing the Bowen-Margulis measure and geodesic flow properties.
result Lebesgue measures of common perpendiculars equidistribute to the Bowen-Margulis measure.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
New algorithm converges to equilibrium in nonconvex-nonconcave optimization problems without dimension dependence.
problem Min-max optimization in nonconvex-nonconcave landscapes.
method Convergent algorithm with greedy max-player updates and proposal distribution for min-player.
result Algorithm converges to equilibrium in non-dependent iterations, suitable for GAN training.
Introduces strong equilibrium for time-inconsistent stopping problems in continuous time.
problem Time-inconsistent stopping problems in continuous time.
method Introduces strong equilibrium, compares with existing mild and weak equilibria, and provides an iteration method to construct optimal mild equilibria.
result Optimal mild equilibria are always strong equilibria under certain conditions.
In order to use the advanced inference techniques available for Ising models, we transform complex data (real vectors) into binary strings, by local averaging and thresholding. This transformation introduces parameters, which must be varied to characterize the behaviour of the system. The approach is illustrated on fin…
Paper proposes incentives for federated learning to ensure truthful contributions.
problem Ensuring truthful contributions from decentralized users in federated learning.
method Introduces a scoring rule based framework to incentivize truthful reporting of local hypotheses at a Bayesian Nash Equilibrium.
result Proposed solution verified using MNIST and CIFAR-10 datasets, showing decreasing scores for low-quality hypotheses.
The paper proves well-posedness of nonlocal PDEs related to stochastic control problems.
problem Characterizing equilibrium strategies and value functions for time-inconsistent stochastic control problems.
method Method of continuity and Banach's fixed point arguments, with Schauder prior estimates.
result Global well-posedness of nonlocal fully nonlinear PDEs with sharp a-priori estimates.
Dynamic sampling from changing graphical models.
problem Sampling from a changing graphical model.
method Parallel Las Vegas algorithm for dynamic sampling.
result First dynamic sampling algorithms for Ising and hardcore models.
New algorithm speeds up network analysis for large datasets.
problem Efficiently estimating models for large network data sets.
method Equilibrium Expectation (EE) algorithm based on Markov chain properties.
result Significantly increased size of networks that can be analyzed using ERGMs.
Let L be a holomorphic line bundle over a compact complex projective Hermitian manifold X. Any fixed smooth hermitian metric h on L induces a Hilbert space structure on the space of global holomorphic sections with values in the k th tensor power of L. In this paper various convergence results are obtained for the corr…
Paper analyzes convergence of GDA for nonconvex-nonconcave minimax problems.
problem Understanding convergence of GDA for nonconvex-nonconcave minimax problems.
method Local convergence analysis of GDA with stepsize ratio Θ(κ).
result Stepsize ratio of Θ(κ) is necessary and sufficient for local convergence of GDA to a Stackelberg Equilibrium.
Two-cycle GEILA equilibria are OLG equilibria and vice versa, with applications to indeterminacy and bubbles.
problem Relationship between GEILA and OLG models.
method Proof of equilibrium equivalence and application to indeterminacy and bubbles.
result GEILA and OLG models are equivalent under certain conditions.
Proposes a new metric for financial risk based on volatility's local deviations.
problem Inefficiencies in classical risk metrics like volatility.
method Introduces pointwise regularity via the Hurst-Holder exponent.
result A more nuanced assessment of market inefficiencies and mechanisms for restoring equilibrium.
We prove the existence of a Radner equilibrium in a model with proportional transaction costs on an infinite time horizon and analyze the effect of transaction costs on the endogenously determined interest rate. Two agents receive exogenous, unspanned income and choose between consumption and investing into an annuity.…
The paper tackles multi-agent inverse reinforcement learning in stochastic games, proposing solutions for five variants.
problem Inverse reinforcement learning in multi-agent stochastic games with different solution concepts.
method Developed novel approaches for five variants of multi-agent inverse reinforcement learning (MIRL) in a two-player general-sum stochastic game framework.
result Proposed solutions for five variants of MIRL: uCS-MIRL, advE-MIRL, cooE-MIRL, uCE-MIRL, and uNE-MIRL.
Study on LOB dynamics using mean-field game theory.
problem Modeling liquidity dynamics in limit order books.
method Mean-field stochastic differential equation and control problem formulation.
result Equilibrium density function of LOB can be derived.
We analyze a monetary system of random money transfer on the basis of double entry bookkeeping. Without boundary conditions, we do not reach a price equilibrium and violate text-book formulas of economists quantity theory (MV=PQ). To match the resulting quantity of money with the model assumption of a constant price, w…
Existence of Radner equilibrium proven with growing population.
problem Analyzing Radner equilibrium in a model with population growth.
method Proved existence of equilibrium for growing population using mathematical analysis.
result Equilibrium exists for a growing population, with effects on annuity prices.
Study how transaction costs impact stock returns and holdings in equilibrium.
problem Impact of quadratic transaction costs on equilibrium stock returns and holdings.
method Developed a continuous-time risk-sharing model with FBSDEs to characterize equilibrium stock holdings and trading rates.
result Equilibrium stock holdings and trading rates are uniquely determined by FBSDEs, and equilibrium return by a system of coupled FBSDEs.
Equilibrium found for multi-agent trading with transaction costs.
problem Designing a trading equilibrium for multiple agents with transaction costs.
method Proving the existence of a continuous-time Radner equilibrium with incentives and transaction costs.
result Each agent optimally trades for a specific time interval before stopping, influenced by transaction costs.
We propose a method for learning cyclic causal models from a combination of observational and interventional equilibrium data. Novel aspects of the proposed method are its ability to work with continuous data (without assuming linearity) and to deal with feedback loops. Within the context of biochemical reactions, we a…
The paper finds unique equilibrium states for geodesic flows on certain surfaces.
problem Analyzing geodesic flows on surfaces without focal points.
method Proving the existence of unique equilibrium states for specific potentials.
result There are unique equilibrium states for certain potentials, including geometric multiples of scalar less than 1.
This paper tackles global Nash equilibrium in non-convex multi-player games.
problem Challenges in finding global Nash equilibrium due to non-convexity.
method Conjugate transformation and variational inequality formulation to prove existence and design algorithms.
result Designs an ODE-based algorithm with exponential convergence rate and proves its effectiveness in practical scenarios.
Study on equilibrium with non-convex preferences.
problem Existence of equilibrium in non-convex preference settings.
method Provided a necessary and sufficient condition for equilibrium existence.
result Standard equilibrium theory cannot be applied to non-convex preferences.
We combine general equilibrium theory and theorie generale of stochastic processes to derive structural results about equilibrium state prices.