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Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used to estimate gradients of expectations throughout machine learning and reinforcement learning; however, they are usually explained as simple mathematical tricks,…
We study infinite-horizon robust Markov decision processes (MDPs) on continuous state spaces with structured rectangular ambiguity set. The proposed ambiguity set falls within the convex hull of unknown generating kernels. We utilize the…
In this paper, a many-sources large deviations principle (LDP) for the transient workload of a multi-queue single-server system is established where the service rates are chosen from a compact, convex and coordinate-convex rate region and…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…
We consider the problem of solving robust Markov decision process (MDP), which involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. The goal of planning is to find a robust policy that…
Partially observable Markov decision processes (POMDPs) provide a flexible representation for real-world decision and control problems. However, POMDPs are notoriously difficult to solve, especially when the state and observation spaces are…
Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using…
Ratings are frequently used to evaluate and compare subjects in various applications, from education to healthcare, because ratings provide succinct yet credible measures for comparing subjects. However, when multiple rating lists are…
We focus on the classification problem with a separable dataset, one of the most important and classical problems from machine learning. The standard approach to this task is logistic regression with gradient descent (LR+GD). Recent studies…
We prove a large deviation principle for the point process associated to $k$-element connected components in $\mathbb R^d$ with respect to the connectivity radii $r_n\to\infty$. The random points are generated from a homogeneous Poisson…
The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have…
Authors of Phys. Rev. Lett. 103, 228702 (2009) claim that "The residual degree gradient (RDG) method can enhance thesynchronizability of networks by simply changing the direction of the links". In this paper, we argue that in some case the…
To overcome the curse of dimensionality and curse of modeling in Dynamic Programming (DP) methods for solving classical Markov Decision Process (MDP) problems, Reinforcement Learning (RL) algorithms are popular. In this paper, we consider…
We build on a recently introduced geometric interpretation of Markov Decision Processes (MDPs) to analyze classical MDP-solving algorithms: Value Iteration (VI) and Policy Iteration (PI). First, we develop a geometry-based analytical…
Typical IRT rating-scale models assume that the rating category threshold parameters are the same over examinees. However, it can be argued that many rating data sets violate this assumption. To address this practical psychometric problem,…
We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures…
Reparameterization (RP) and likelihood ratio (LR) gradient estimators are used throughout machine and reinforcement learning; however, they are usually explained as simple mathematical tricks without providing any insight into their nature.…
Markov decision process (MDP) is a decision making framework where a decision maker is interested in maximizing the expected discounted value of a stream of rewards received at future stages at various states which are visited according to…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
Multilayer perceptron (MLP), one of the most fundamental neural networks, is extensively utilized for classification and regression tasks. In this paper, we establish a new generalization error bound, which reveals how the variance of…