A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
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 N-player games by mean-field control and mean-field equilibria.
This paper tackles sample-efficient reinforcement learning for partially observable Markov games.
problem Learning in partially observable Markov games with incomplete information.
method A simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) for self-play, and a variant of optimistic MLE for adversarial opponents.
result The proposed algorithms achieve approximate Nash, correlated, and coarse correlated equilibria in polynomial samples for weakly revealing POMGs.
New MARL algorithms resolve the curse of multiagency with function approximation.
problem Challenges in Multi-Agent Reinforcement Learning (MARL) due to the curse of multiagency.
method V-Learning with Policy Replay and Decentralized Optimistic Policy Mirror Descent.
result First polynomial sample complexity results for learning approximate Coarse Correlated Equilibria (CCEs) of Markov Games under decentralized linear function approximation.
New algorithms for RL in Markov games with independent linear function approximation, breaking the curse of multiagents.
problem Tackles the challenge of learning Markov equilibria in large state space Markov games with multiple agents.
method Proposes independent linear Markov games and designs new algorithms for learning Markov coarse correlated equilibria and Markov correlated equilibria with polynomial sample complexity.
result Breaks the curse of multiagents by achieving sample complexity bounds that scale polynomially with each agent's function class complexity.
Temporal coarse-graining of latent default paths explains effective correlation in corporate defaults.
problem Understanding effective default correlation in corporate defaults.
method Temporal coarse-graining of latent default-probability paths, applied to corporate default-count data.
result Temporal coarse-graining provides a scale-consistent baseline that improves identifiability and reduces over-allocation of long-horizon fluctuations.
The notion of \emph{policy regret} in online learning is a well defined? performance measure for the common scenario of adaptive adversaries, which more traditional quantities such as external regret do not take into account. We revisit the notion of policy regret and first show that there are online learning settings …
We introduce a quantitative approach to comparative statics that allows to bound the maximum effect of an exogenous parameter change on a system's equilibrium. The motivation for this approach is a well known paradox in multimarket Cournot competition, where a positive price shock on a monopoly market may actually redu…
The existence of stationary Markov perfect equilibria in stochastic games is shown under a general condition called "(decomposable) coarser transition kernels". This result covers various earlier existence results on correlated equilibria, noisy stochastic games, stochastic games with finite actions and state-independe…
Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of recent advances in equilibrium computation for probabilistic inference. We present formulations of inference problems in Markov random f…
We study constrained nonconvex optimization problems in machine learning, signal processing, and stochastic control. It is well-known that these problems can be rewritten to a minimax problem in a Lagrangian form. However, due to the lack of convexity, their landscape is not well understood and how to find the stable e…
We propose a new approach for analyzing price fluctuations in their strongly correlated regime ranging from minutes to months. This is done by employing a self-similarity assumption for the magnitude of coarse-grained price fluctuation or volatility. The existence of a Cramer function, the characteristic function for s…
Although there has been a rapid development of practical applications, theoretical explanations of deep learning are in their infancy. Deep learning performs a sophisticated coarse graining. Since coarse graining is a key ingredient of the renormalization group (RG), RG may provide a useful theoretical framework direct…
Quantized deep neural networks (QDNNs) are attractive due to their much lower memory storage and faster inference speed than their regular full precision counterparts. To maintain the same performance level especially at low bit-widths, QDNNs must be retrained. Their training involves piecewise constant activation func…
We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n→∞. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that me…
The study examines different types of equilibria for stopping problems in one-dimensional diffusion processes.
problem Characterizing and comparing different types of equilibria for time-inconsistent stopping problems.
method Analyzes log sub-additive discount functions and one-dimensional diffusion processes to derive necessary and sufficient conditions for weak equilibria and other types of equilibria.
result Conditions for weak equilibria and their implications for other types of equilibria are provided.
We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due to the existence of non-Nash stationary points. By taking advantage of the differ…
For a symmetric Hamiltonian system, lower bounds for the number of relative equilibria surrounding stable and formally unstable relative equilibria on nearby energy levels are given.
We propose a probabilistic model for refining coarse-grained spatial data by utilizing auxiliary spatial data sets. Existing methods require that the spatial granularities of the auxiliary data sets are the same as the desired granularity of target data. The proposed model can effectively make use of auxiliary data set…
A new definition of continuous-time equilibrium controls is introduced. As opposed to the standard definition, which involves a derivative-type operation, the new definition parallels how a discrete-time equilibrium is defined, and allows for unambiguous economic interpretation. The terms "strong equilibria" and "weak …
We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price acc…
We prove a criterion for stability of relative equilibria in symmetric Hamiltonian systems at singular points of the momentum map. This generalizes a theorem of G.W. Patrick. The method of the proof is also useful in studying the bifurcation of relative equilibria.