arXiv research

New offline RL method works with limited data and function approximators.

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

New convergence rates for shuffling gradient methods without strong convexity.

Logarithmic regret achieved in RL with linear function approximation.

N-discount optimality was introduced as a hierarchical form of policy- and value-function optimality, with Blackwell optimality lying at the top level of the hierarchy Veinott (1969); Blackwell (1962). We formalize notions of myopic discount factors, value functions and policies in terms of Blackwell optimality in MDPs…

This paper shows how to solve complex reinforcement learning problems with zero duality gap.

New estimates show spectral gap stability in RCD spaces, close to Beta distribution.

This paper develops a pricing model for data assets from the buyer's perspective.

We consider the classical optimal dividends problem under the Cramér-Lundberg model with exponential claim sizes subject to a constraint on the time of ruin. We introduce the dual problem and show that the complementary slackness conditions are satisfied, thus there is no duality gap. Therefore the optimal value functi…

New kernels capture both local and non-local interactions efficiently.

FFBO optimizes functions as inputs and outputs, improving on existing BO methods.

Temporal difference learning and Residual Gradient methods are the most widely used temporal difference based learning algorithms; however, it has been shown that none of their objective functions is optimal w.r.t approximating the true value function $V$. Two novel algorithms are proposed to approximate the true value…

Study estimates gaps in semigroup products, proving embedding properties.

Investigates optimal PPI strategies in jump-diffusion models to mitigate downside risk.

In this paper we study some new von Neumann spectral invariants associated to the Laplacian acting on L^2 differential forms on the universal cover of a closed manifold. These invariants coincide with the Novikov-Shubin invariants whenever there is no spectral gap in the spectrum of the Laplacian, and are homotopy inva…

Develops vector-valued RKBS for neural networks and operators.

Several recently proposed architectures of neural networks such as ResNeXt, Inception, Xception, SqueezeNet and Wide ResNet are based on the designing idea of having multiple branches and have demonstrated improved performance in many applications. We show that one cause for such success is due to the fact that the mul…

New method quantifies uncertainty in reinforcement learning models.

This work optimizes bid strategies for online auctions using measure-valued optimization.

This paper provides lower bounds on the convergence rate of Derivative Free Optimization (DFO) with noisy function evaluations, exposing a fundamental and unavoidable gap between the performance of algorithms with access to gradients and those with access to only function evaluations. However, there are situations in w…

New lower bound shows RL with linear approximations is computationally hard.

Optimizes target value in stochastic black box functions.

Cubic-regularized Newton's method (CR) is a popular algorithm that guarantees to produce a second-order stationary solution for solving nonconvex optimization problems. However, existing understandings of the convergence rate of CR are conditioned on special types of geometrical properties of the objective function. In…

We propose a flexible method for estimating value functions in reinforcement learning without parametric assumptions.

Reply to Tetlock et al. on tail risk and probability gap.

As shown in recent research, deep neural networks can perfectly fit randomly labeled data, but with very poor accuracy on held out data. This phenomenon indicates that loss functions such as cross-entropy are not a reliable indicator of generalization. This leads to the crucial question of how generalization gap should…

New study shows exponential lower bound for RL even with constant suboptimality gap.

Proposes a meta-learning method for Bayesian optimization with neural network kernels.

Deep, wide ConvResNets can approximate functions and their smoothness.

Study revisits AdaGrad convergence with relaxed noise assumptions.

Unified approach optimizes neural network training for various metrics.

New technique reduces imitation learning performance gap in finite samples.

Efficient reinforcement learning for simultaneous-move zero-sum games using optimistic value iteration.

Isobenefit Lines can offer a certain range of applicability in Location Theory and Gravitational Models for Urban and Geography Economics, in positional decision processes made by citizens, and, last but not least, in land value and property market theories and analysis. The value of a land, or a property, in a generic…

Improved gap-dependent bounds for reinforcement learning with linear approximations.

Estimates generalization gap for overparameterized models using Langevin approximation.

SurVAE Flows combine VAEs and flows using surjective transformations.

We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for holomorphic maps from elliptic curves to the complex projective space, and study th…

This paper tackles learning Stackelberg equilibrium in asymmetric games efficiently from noisy samples.

The paper analyzes the latent geometry of generative diffusion models.

The paper analyzes risk bounds and Rademacher complexity in batch RL.

The study uses Random Matrix Theory to identify structural changes in stock markets during shocks.

We propose two methods for exact Gaussian process (GP) inference and learning on massive image, video, spatial-temporal, or multi-output datasets with missing values (or "gaps") in the observed responses. The first method ignores the gaps using sparse selection matrices and a highly effective low-rank preconditioner is…

Proves convexity of certain hypersurfaces with negative λ.

We introduce a longevity feature to the classical optimal dividend problem by adding a constraint on the time of ruin of the firm. We extend the results in \cite{HJ15}, now in context of one-sided Lévy risk models. We consider de Finetti's problem in both scenarios with and without fix transaction costs, e.g. taxes. We…

Attributing forecast gaps to component models in complex model suites

Local gap theorem for Ricci shrinkers ensures flatness if certain functionals are close to zero.

The paper tackles attributing forecast gaps in complex model suites.