arXiv research

The paper analyzes Q-learning in 2-player Markov games and provides gap-dependent logarithmic regret bounds.

This paper establishes that optimistic algorithms attain gap-dependent and non-asymptotic logarithmic regret for episodic MDPs. In contrast to prior work, our bounds do not suffer a dependence on diameter-like quantities or ergodicity, and smoothly interpolate between the gap dependent logarithmic-regret, and the $\wid…

Paper uses ABP method to prove logarithmic Sobolev inequalities on curved spaces.

Study heat flow on changing surfaces, proving existence and uniqueness.

The paper addresses portfolio allocation with uncertain covariance matrices, finding a logarithmic risk dependence.

Finite-time queue peaks in stochastic networks have logarithmic scaling after geometric thresholds.

We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the RecursiveTensorSketch [Ahle et al. SODA 2020]. After providing concentration and approximation pro…

Algorithm reduces regret in multi-player bandits with unknown collision rewards.

We find a nonlinear dependence between an indicator of the degree of multiscaling of log-price time series of a stock and the average correlation of the stock with respect to the other stocks traded in the same market. This result is a robust stylized fact holding for different financial markets. We investigate this re…

Logarithmic regret for continuous-time reinforcement learning.

We study the problem of regret minimization for distributed bandits learning, in which $M$ agents work collaboratively to minimize their total regret under the coordination of a central server. Our goal is to design communication protocols with near-optimal regret and little communication cost, which is measured by the…

The paper finds that circles and logarithmic spirals are the only constant-speed ramps for a specific force field.

Abstract: New geometric incarnation of isomonodromy functors.

Logarithmic regret achieved in continuous-time linear-quadratic reinforcement learning.

Derives gradient estimate for a specific nonlinear parabolic equation on Finsler manifolds.

Local logarithmic export distributions show non-zero skewness that changes with exporter and destination characteristics.

We make an extensive empirical study of the market impact of large orders (metaorders) executed in the U.S. equity market between 2007 and 2009. We show that the square root market impact formula, which is widely used in the industry and supported by previous published research, provides a good fit only across about tw…

This paper gives quantitative global estimates between a time dependent flow on a Riemannian manifold $\left( M\right)$ and the flow of a vector field constructed by truncating the formal Magnus expansion for the logarithm of the flow. As a corollary, we also find quantitative estimates between the composition of the …

Logarithmic regret achieved in RL with linear function approximation.

New algorithm reduces regret for many bandit algorithms with logarithmic dependence on number of algorithms.

We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price. Previously, this was proven for the case of the Gaussian logarithmic returns model by Harrison and Kreps, but we prove …

New Thompson sampling algorithm for stochastic partial monitoring achieves logarithmic regret.

Study optimal policy regret in partially observable Markov games with adaptive opponents.

New bounds for online portfolio selection without smoothness assumptions.

We derive a logarithmic Sobolev inequality along the Ricci flow without any restriction on time, which depends only on the initial metric via rudimentary geometric data, assuming only that a certain first eigenvalue is positive. As a consequence we obtain a uniform Sobolev inequality along the Ricci flow without any re…

The paper explores the geometric structure of cost functions in multiple dimensions.

A relation between the conformal anomaly and the logarithmic term in the entanglement entropy is known to exist for CFT's in even dimensions. In odd dimensions the local anomaly and the logarithmic term in the entropy are absent. As was observed recently, there exists a non-trivial integrated anomaly if an odd-dimensio…

Study calculates quantum hyperbolic invariants for figure-eight knot complement, finding it either 0 or half the volume.

Study robust utility maximization with uncertain continuous semimartingales.

The common assumption of universal behavior in stock market data can sometimes lead to false conclusions. In statistical physics, the Hurst exponents characterizing long-range correlations are often closely related to universal exponents. We show, that in the case of time series of the traded value, these Hurst exponen…

New bounds for Bayesian bandits show prior improves performance.

Bounding shears in ideal triangulations on hyperbolic surfaces.

New algorithm reduces bandit problem's regret bound to logarithmic in dimension.

This work improves the convergence theory of diffusion models for generating samples from complex distributions.

Logarithmic regret strategies for safe multi-armed bandits with safety risk constraints.

Paper proves tight lower bounds for online multicalibration, separating it from marginal calibration.

Paper proposes DG-ETC for online submodular maximization with stochastic bandit feedback.

Gaussian Graphical Models (GGMs) have wide-ranging applications in machine learning and the natural and social sciences. In most of the settings in which they are applied, the number of observed samples is much smaller than the dimension and they are assumed to be sparse. While there are a variety of algorithms (e.g. G…

Study sparsity benefits in infinite feature contextual bandits.

Let $(X, D)$ be a logarithmic pair, and let $h$ be a singular metric on the tangent bundle, smooth on the open part of $X$. We give sufficient conditions on the curvature of $h$ for the logarithmic and the standard cotangent bundles to be big. As an application, we give a metric proof of the bigness of logarithmic cota…

Decentralized learning for matching markets with time-varying preferences.

New algorithms improve causal graph discovery with adaptive interventions, even under worst-case interventional costs.

New algorithm reduces regret in asynchronous multiplayer bandits to constant or logarithmic levels.

Ancient Ricci flows with asymptotic solitons have uniform bounds and inequalities.

Study gap-dependent regret bounds for risk-sensitive RL.

The paper develops a robust algorithm for contextual bandits with heavy-tailed rewards.

Study on regret minimization in deterministic MDPs.

Gradient descent optimally trains RNNs without overparameterization.