Related papers: Automated Tail Bound Analysis for Probabilistic Re…
We propose a novel constrained reinforcement learning method for finding optimal policies in Markov Decision Processes while satisfying temporal logic constraints with a desired probability throughout the learning process. An…
Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited…
The trapping redundancy of a linear code is the number of rows of a smallest parity-check matrix such that no submatrix forms an $(a,b)$-trapping set. This concept was first introduced in the context of low-density parity-check (LDPC) codes…
A common bottleneck in evaluating extremal performance measures is that, due to their very nature, tail data are often very limited. The conventional approach selects the best probability distribution from tail data using parametric…
Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixing and mixture densities are consistent under fairly mild…
This paper investigates the optimality analysis of the recursive least-squares (RLS) algorithm for autoregressive systems with exogenous inputs (ARX systems). A key challenge in analyzing is managing the potential unboundedness of the…
We introduce a method to estimate simultaneously the tail and the threshold parameters of an extreme value regression model. This standard model finds its use in finance to assess the effect of market variables on extreme loss distributions…
Gradient clipping is a commonly used technique to stabilize the training process of neural networks. A growing body of studies has shown that gradient clipping is a promising technique for dealing with the heavy-tailed behavior that emerged…
We establish sharp estimates for the convergence rate of the Kranosel'ski\v{\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of…
Reinforcement Learning (RL) for Large Language Models (LLMs) faces a fundamental tension: the numerical divergence between high-throughput inference engines and numerically precise training engines. Although these systems share the same…
In this work, we propose a class of importance sampling (IS) estimators for estimating the right tail probability of a sum of continuous random variables based on a change of variables to $L^1$ polar coordinates in which the radial and…
We propose a variational tail bound for norms of random vectors under moment assumptions on their one-dimensional marginals. A simplified version of the bound that parametrizes the ``aggregating distribution'' using a certain pushforward of…
Given the damping factor $\alpha$ and precision tolerance $\epsilon$, \citet{andersen2006local} introduced Approximate Personalized PageRank (APPR), the \textit{de facto local method} for approximating the PPR vector, with runtime bounded…
Large Language Models (LLMs) exhibit remarkable proficiency in addressing a diverse array of tasks within the Natural Language Processing (NLP) domain, with various prompt design strategies significantly augmenting their capabilities.…
Probabilistic forecasts comprehensively describe the uncertainty in the unknown future outcome, making them essential for decision making and risk management. While several methods have been introduced to evaluate probabilistic forecasts,…
We propose an automata-theoretic approach for reinforcement learning (RL) under complex spatio-temporal constraints with time windows. The problem is formulated using a Markov decision process under a bounded temporal logic constraint.…
We propose a new method to approximate the posterior distribution of probabilistic programs by means of computing guaranteed bounds. The starting point of our work is an interval-based trace semantics for a recursive, higher-order…
Markov decision processes (MDPs) with large number of states are of high practical interest. However, conventional algorithms to solve MDP are computationally infeasible in this scenario. Approximate dynamic programming (ADP) methods tackle…
By combining several interesting applications of random sampling in geometric algorithms like point location, linear programming, segment intersections, binary space partitioning, Clarkson and Shor \cite{CS89} developed a general framework…
We consider the tail probabilities of stock returns for a general class of stochastic volatility models. In these models, the stochastic differential equation for volatility is autonomous, time-homogeneous and dependent on only a finite…