arXiv research

We solve offline learning problems without action probabilities using imitation and policy improvement.

A new calibration metric bridges testability and actionability.

The paper introduces metrics to rank potential outcomes for better decision-making.

Study positive entropy actions by higher-rank lattices, proving rigidity and conjugacy results.

Safe actions learned in finite trials, without infinite exploration.

Develops a machine learning framework for computing most probable paths in stochastic systems.

Deep Reinforcement Learning improves with Weighted Q-Learning to reduce bias and uncertainty.

In this paper, we show that the Euler characteristic of an even dimensional closed projectively flat manifold is equal to the total measure which is induced from a probability Borel measure on RP^n invariant under the holonomy action, and then discuss its consequences and applications. As an application, we show that t…

New framework for reinforcement learning with sporadic state observations.

In this note we prove the a pointwise ergodic theorem for functions taking values in a separable complete CAT(0)-space, analogous to Lindenstrauss' pointwise ergodic theorem for real-valued integrable functions on a probability space subject to a probability-preserving action of an amenable l.c.s.c. group, where in the…

Paper studies zero-sum games with noisy observations and identifies equilibrium conditions.

The study proves curvature bounds for quotient spaces of isometric actions.

This paper explores the possibility that asset prices, especially those traded in large volume on public exchanges, might comply with specific physical laws of motion and probability. The paper first examines the basic dynamics of asset price displacement and finds one can model this dynamic as a harmonic oscillator at…

Let $M_1$ and $M_2$ be two $n$-dimensional smooth manifolds with boundary. Suppose we glue $M_1$ and $M_2$ along some boundary components (which are, therefore, diffeomorphic). Call the result $N.$ If we have a group $G$ acting continuously on $M_1,$ and also acting continuously on $M_2,$ such that the actions are comp…

LITE efficiently estimates Gaussian PoM with linear time and memory complexity.

A textbook on machine learning explaining patterns, predictions, and actions.

New result on group actions in CAT(0) spaces with vanishing escape rate.

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficul…

The study explores geodesics and KL-divergence on Hölder equilibrium probabilities.

We propose an analytically tractable variation of the minority game in which rational agents use probabilistic strategies. In our model, $N$ agents choose between two alternatives repeatedly, and those who are in the minority get a pay-off 1, others zero. The agents optimize the expectation value of their discounted fu…

This work formalizes robustness criteria for reinforcement learning actions and improves performance in perturbed environments.

Given a Kähler manifold $(Z,J,ω)$ and a compact real submanifold $M\subset Z$, we study the properties of the gradient map associated with the action of a noncompact real reductive Lie group ${\rm G}$ on the space of probability measures on $M.$ In particular, we prove convexity results for such map when ${\rm G}$ is A…

New calibration measure SCDL improves trust in AI predictions.

The isotropy action on certain symmetric spaces is shown to be equivariantly formal.

A scheme robust to action erasures improves MAB performance.

Develops a dynamic mean field theory for reinforcement learning.

We study the sparse entropy-regularized reinforcement learning (ERL) problem in which the entropy term is a special form of the Tsallis entropy. The optimal policy of this formulation is sparse, i.e.,~at each state, it has non-zero probability for only a small number of actions. This addresses the main drawback of the …

Let S be a non-exceptional oriented surface of finite type. We discuss the action of subgroups of the mapping class group of S on the CAT(0)-boundary of the completion of Teichmueller space with respect to the Weil-Petersson metric. We show that the set of invariant Borel probability measures for the Weil-Petersson flo…

Study on information cascade fragility under mismatched revealing probabilities.

A new framework for offline RL improves policy flexibility and regularity.

A new method estimates multi-dimensional value distributions using Hilbert space embeddings.

This paper uses probability tensors for efficient path planning in complex scenarios.

On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher--Rao metric.

We study the problem of learning Markov decision processes with finite state and action spaces when the transition probability distributions and loss functions are chosen adversarially and are allowed to change with time. We introduce an algorithm whose regret with respect to any policy in a comparison class grows as t…

A new method for continuous control avoids local movement issues.

We introduce a new class of reinforcement learning methods referred to as {\em episodic multi-armed bandits} (eMAB). In eMAB the learner proceeds in {\em episodes}, each composed of several {\em steps}, in which it chooses an action and observes a feedback signal. Moreover, in each step, it can take a special action, c…

Central limit theorem for Green metrics on hyperbolic groups.

Efficient algorithms identify true hypothesis from many options with minimal actions.

Uplift modeling is an area of machine learning which aims at predicting the causal effect of some action on a given individual. The action may be a medical procedure, marketing campaign, or any other circumstance controlled by the experimenter. Building an uplift model requires two training sets: the treatment group, w…

A new method combines online and offline learning to tackle contextual bandits with missing action support.

New complexity analysis for estimating normalizing constants in high dimensions.

TRAiL is a linear bandit algorithm that ensures optimal regret and guarantees inference quality.

Develops CLTs for Markov chain transition probabilities and policies.

DG improves policy gradients by weighting actions with a sigmoid of advantage and surprisal.

RegFlow models future states with flexible probability distributions.

Safe imitation learning with a safety layer for flexible training.

Let $(M,ω)$ be a Kähler manifold and let $K$ be a compact group that acts on $M$ in a Hamiltonian fashion. We study the action of $K^\mathbb{C}$ on probability measures on $M$. First of all we identify an abstract setting for the momentum mapping and give numerical criteria for stability, semi-stability and polystabili…

Study geometric and representation theory of statistical transformation models.