Extends LIBOR market model to reduce exploding scenarios.
problem Exploding scenarios in market-consistent guarantees valuation.
method Mean-field extension of the LIBOR market model.
result Existence and uniqueness of MF-LMM proved.
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48 results for “mean-field consistency”
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.
Equilibrium pricing of securities in the co-presence of cooperative and non-cooperative populationsq-fin.MF
Develops an equilibrium model for securities pricing in a mixed cooperative and non-cooperative market.
problem Equilibrium pricing of securities in a market with cooperative and non-cooperative agents.
method Conditional extended mean-field control for cooperative agents, mean-field model for both cooperative and non-cooperative agents.
result Existence of a unique equilibrium for both finite-agent and mean-field models under certain conditions.
ALO-CV approximates leave-one-out error in proportional regime.
problem Estimating generalization error in high-dimensional settings.
method Developed new analysis for ALO-CV, showed consistency under strong convexity.
result ALO-CV approximates leave-one-out error up to negligible error.
Nonnegative Boltzmann machines (NNBMs) are recurrent probabilistic neural network models that can describe multi-modal nonnegative data. NNBMs form rectified Gaussian distributions that appear in biological neural network models, positive matrix factorization, nonnegative matrix factorization, and so on. In this paper,…
We study the mean field games equations, consisting of the coupled Kolmogorov-Fokker-Planck and Hamilton-Jacobi-Bellman equations. The equations are complemented by initial and terminal conditions. It is shown that with some specific choice of data, this problem can be reduced to solving a quadratically nonlinear syste…
Study shows finite agent equilibrium converges to mean-field limit in asset pricing.
problem Asset pricing equilibrium in markets with finite vs infinite agents.
method Existence of finite agent equilibrium and strong convergence to mean-field limit.
result Finite agent equilibrium converges to mean-field limit under suitable conditions.
New method for handling multi-dimensional singular controls with jump costs in mean-field problems.
problem Handling jump costs in multi-dimensional singular controls.
method Introducing two-layer parametrisations to interpolate jumps on both distributional and pathwise levels.
result Derivation of a DPP and characterisation of the value function as a minimal super-solution to a quasi-variational inequality.
Model analyzes competitive pricing strategies in large markets of perishable products.
problem Maximizing profits in a competitive market of perishable products.
method Mean-field competition model, Hamilton-Jacobi-Bellman equation, iterative numerical algorithm.
result Properties of equilibrium pricing strategies and market dynamics.
Mean-field game of mean-variance portfolio management with peer-based relative risk aversionq-fin.MF
New MFG model for MV portfolio management with peer-based risk aversion.
problem Time-inconsistent mean-variance portfolio management with peer-based risk aversion.
method Mean-field game, smooth regularization, fixed-point arguments, convergence analysis.
result Existence of mean-field equilibrium in time-inconsistent MFG.
Learning interaction kernels in mean-field equations of 1st-order systems of interacting particlesstat.ML
Algorithm learns interaction kernels for particle systems from data.
problem Understanding and modeling interactions in systems of interacting particles.
method Nonparametric algorithm using least squares with regularization, probabilistic error functional, and reproducing kernel Hilbert space convergence.
result The algorithm converges optimally and accurately learns interaction kernels.
We study ranking quantilized mean-field games to select top-performing agents.
problem Selecting top-performing agents in competitive scenarios.
method Developed two formulations: target-based and threshold-based, and provided analytic and semi-explicit solutions.
result Analytic and semi-explicit solutions for quantilized mean-field consistency conditions.
Study on price formation in a market with a major player and minor firms.
problem Equilibrium price formation in a market with a major financial firm and many minor firms.
method Analyzes the equilibrium price process in both finite and mean field models, considering idiosyncratic and common noises.
result Derives the functional form of price impact for the major firm in both market sizes.
Analysis of SGD for Gaussian mixture classification using dynamical mean-field theory.
problem Learning dynamics of SGD for a neural network classifying Gaussian mixture.
method Applying dynamical mean-field theory to track SGD dynamics in high dimensions.
result Reveals how SGD navigates the non-convex loss landscape.
Paper analyzes Transformer learning dynamics, proving benign landscape for in-context learning.
problem Understanding how Transformers learn in context with nonlinear features.
method Mean-field and two-timescale analysis of Transformer dynamics, proving nonconvex but benign landscape.
result Proves mean-field dynamics avoid saddle points, leading to improved optimization.
In his lectures at College de France, P.L. Lions introduced the concept of Master equation, see [5] for Mean Field Games. It is introduced in a heuristic fashion, from the system of partial differential equations, associated to a Nash equilibrium for a large, but finite, number of players. The method, also explained in…
Paper studies optimal tracking portfolio in mean field game of large fund competition.
problem Optimal tracking portfolio in large fund competition with relative performance benchmark.
method Formulated mean field game problem, established existence of mean field equilibrium using PDE approach, constructed approximate Nash equilibrium.
result Existence of mean field equilibrium and consistency condition verified.
New method infers population dynamics from snapshots using path space optimization.
problem Recover dynamics of a population from its temporal marginals.
method Grid-free algorithm using Schrödinger bridges coupled via noisy gradient descent in mean-field limit.
result Global convergence to min-entropy estimator with end-to-end theoretical guarantees.
The paper analyzes the dynamics of a simple neural network using a mean-field approach.
problem Understanding the training dynamics of neural networks, especially in classification tasks.
method Developed an analytic theory using a mean-field limit for a simple neural network.
result Explicitly solved the dynamics of a linearly separable dataset with a linear hinge loss.
This paper studies insurers' robust strategies in a stochastic game with model uncertainty and volatility risk.
problem Model uncertainty and volatility risk in insurers' surplus processes.
method Formulates robust mean-field games with insurers competing based on mean-variance criterion under worst-case scenario.
result Derives semi-closed forms of equilibrium strategies for insurers and mean-field equilibrium, ensuring existence and uniqueness.
Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computationstat.ML
New method improves approximate inference for Bayesian models.
problem Approximate inference for high-dimensional Bayesian models.
method Entropic regularization of mean-field variational inference.
result Improved recovery of true posterior dependency.
New method for high-dimensional linear regression using empirical Bayes.
problem Estimating prior in high-dimensional linear regression.
method Variational empirical Bayes approach with NPMLE and mean field approximation.
result Established asymptotic consistency and computational efficiency of the method.
A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In th…
Infinite-Dimensional LQ Mean Field Games with Common Noise: Small and Arbitrary Finite Time Horizonsmath.OC
Developed LQ MFG theory with common noise, proving existence and uniqueness.
problem Linear-quadratic mean field games with common noise.
method Coupled forward-backward stochastic evolution equations (FBSEEs) in Hilbert spaces.
result Existence and uniqueness of solutions for small and arbitrary finite time horizons.
MF-PID uses interacting samples to efficiently transport probability mass.
problem Efficiently transporting probability mass in generative models.
method Introducing Mean-Field Path-Integral Diffusion (MF-PID) where samples become interacting agents.
result MF-PID achieves 19-24% reductions in control energy for demand-response control of energy systems.
PDA method optimizes neural networks with global convergence rate analysis.
problem Quantitative convergence rate for neural network optimization in mean field regime.
method Particle dual averaging (PDA) method, combining Langevin algorithm and outer loop optimization.
result Established quantitative global convergence for two-layer mean field neural networks.
Compact parameterization improves Bayesian neural network performance.
problem Improving performance of Bayesian neural networks using variational methods.
method Restricting variational distribution to a k-tied Normal distribution with low-rank factorization.
result Compact parameterization improves signal-to-noise ratio and convergence speed.
Modeling DEX liquidity with heterogeneous LPs and MEV bots.
problem Understanding and predicting the dynamics of decentralized cryptocurrency exchanges.
method Mean-field game approach to model liquidity providers' optimal strategies and interactions.
result Calibrated model produces consistent pool exchange rate dynamics and liquidity evolution.
Paper adds Fisher Information to mean field optimization for faster convergence.
problem Mean field optimization in neural networks training.
method Developed energy-dissipation method and gradient flow on probability space.
result Marginal distributions converge exponentially to minimizer.
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph part…
Study explores optimal strategies in games with multiple players and mean-field interactions.
problem Optimal strategies in games with multiple players and mean-field interactions.
method Exploration of three different notions of optimality, including mean-field control solution, mean-field coarse correlated equilibria, and mean-field Nash equilibria.
result Approximation of cooperative and competitive equilibria in large -player games by mean-field control and mean-field equilibria.
Study optimal treatment assignment policies under strategic agent responses.
problem Learning optimal treatment policies with strategic agents complicates estimation.
method Dynamic model with threshold convergence to mean-field equilibrium, consistent estimator for policy gradient.
result Threshold for treatment assignment converges to mean-field equilibrium threshold under large but finite number of agents.
Study on investment strategy for agents with periodic preferences and discounting.
problem Investment decisions by agents with periodic S-shaped preferences and present bias.
method Infinite-horizon, continuous-time portfolio selection problem with quasi-hyperbolic discounting.
result Time-consistent planning strategy can be formulated as an equilibrium to a static mean field game.
A framework solves parametric families of MFGs efficiently.
problem Efficiently solving MFG systems with varying initial distributions and terminal costs.
method Operator learning framework for parametric families of MFGs.
result Accurate approximation for cybersecurity and quadratic MFGs.
Generative diffusion models exhibit phase transitions in statistical mechanics, impacting their performance.
problem Understanding the performance and capabilities of generative diffusion models.
method Reformulating generative diffusion models using statistical mechanics, focusing on phase transitions and symmetry breaking.
result Generative diffusion models undergo second-order phase transitions with mean-field universality, critical instability, and mean-field critical exponents.
This paper investigates Frequentist consistency properties of the posterior distributions constructed via Generalized Variational Inference (GVI). A number of generic and novel strategies are given for proving consistency, relying on the theory of -convergence. Specifically, this paper shows that under minimal regul…
Unified q-learning for mean-field jump-diffusion models with unobservable population distribution.
problem Continuous-time q-learning in mean-field jump-diffusion models with unobservable population distribution.
method Proposed decoupled Iq-function for unified policy evaluation in MFG and MFC problems; unified q-learning algorithm based on test policies and averaged martingale orthogonality condition.
result Unified policy evaluation rule for MFG and MFC problems based on decoupled Iq-function.
Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noisemath.OC
Existence of strong randomized equilibria in mean-field games with common noise.
problem Existence of strong solutions in mean-field games of optimal stopping.
method Connection with Bank-El Karoui's representation problem and continuity assumptions.
result Existence of strong randomized mean-field equilibrium under certain conditions.
New RL algorithms achieve optimal policies with polynomial sample complexity for mean-field problems.
problem Statistical efficiency of Mean-Field Reinforcement Learning with general function approximation.
method Introduce MF-MBED to characterize problem complexity, propose algorithms based on maximal likelihood estimation.
result Rich mean-field RL problems have low MF-MBED, leading to polynomial sample complexity.
Elman-type RNNs converge to globally optimal solutions in the mean-field regime.
problem Optimizing feature learning in wide RNNs.
method Analysis of gradient descent dynamics and mean-field limits.
result Fixed points of infinite-width dynamics are globally optimal.
Batch Normalization (BatchNorm) is an extremely useful component of modern neural network architectures, enabling optimization using higher learning rates and achieving faster convergence. In this paper, we use mean-field theory to analytically quantify the impact of BatchNorm on the geometry of the loss landscape for …
Model predicts stationary equilibrium in investment decisions of firms in fluctuating markets.
problem Investment decisions in fluctuating markets with varying volatility and commodity prices.
method Mean-field model with Gaussian productivity shocks and two-state Markov chain for macroeconomic events.
result Existence, uniqueness, and characterization of stationary mean-field equilibrium with barrier-type investment strategy.
Study on mean field games with singular controls and their applications.
problem Optimal productivity expansion in dynamic oligopolies.
method Existence and uniqueness of mean field equilibria through nonlinear equations, Abelian limit for discounted and ergodic games.
result Valid connection between discounted and ergodic games, approximation of Nash equilibria.
Study shows uniform-time chaos propagation in mean field Langevin dynamics.
problem Understanding the convergence of marginal distributions in mean field dynamics.
method Assumed functional convexity of energy, used -convergence and Wasserstein metrics.
result Uniform-in-time propagation of chaos proved in both -Wasserstein and relative entropy.
Mean-Field Networkscs.LG
The mean field algorithm is a widely used approximate inference algorithm for graphical models whose exact inference is intractable. In each iteration of mean field, the approximate marginals for each variable are updated by getting information from the neighbors. This process can be equivalently converted into a feedf…
New SDEs use -Brownian motion, extending mean-field models.
problem Extending mean-field models to new types of stochastic processes.
method Introduced -SDEs with coefficients dependent on current state and solution as random variable.
result Validated new SDE framework for complex stochastic systems.
Geometric framework analyzes bias in variational inference for posterior functionals.
problem Analyzing the bias of posterior functionals under variational approximations.
method Developed a geometric framework to evaluate the bias of posterior functionals using the variational tangent space.
result The leading-order bias of a posterior functional is determined by its component orthogonal to the variational tangent space.
New neural networks learn mappings between probability measures and functions.
problem Learning mappings between Wasserstein space of probability measures and function spaces.
method Two types of neural networks: bin density and cylindrical approximation, are proposed and supported by universal approximation theorems.
result Accuracy and efficiency of mean-field neural networks in generalization error with various test distributions.