Related papers: The Rectilinear Marco Polo Problem
Laplacian-based methods are popular for the dimensionality reduction of data lying in $\mathbb{R}^N$. Several theoretical results for these algorithms depend on the fact that the Euclidean distance locally approximates the geodesic distance…
Ensuring AI models align with human values is essential for their safety and functionality. Reinforcement learning from human feedback (RLHF) leverages human preferences to achieve this alignment. However, when preferences are sourced from…
Exploration in unknown environments is a fundamental problem in reinforcement learning and control. In this work, we study task-guided exploration and determine what precisely an agent must learn about their environment in order to complete…
While policy-based reinforcement learning (RL) achieves tremendous successes in practice, it is significantly less understood in theory, especially compared with value-based RL. In particular, it remains elusive how to design a provably…
Optimal transport (OT) has recently found widespread interest in machine learning. It allows to define novel distances between probability measures, which have shown promise in several applications. In this work, we discuss how to…
We present a new class of service for location based social networks, called the Flexible Group Spatial Keyword Query, which enables a group of users to collectively find a point of interest (POI) that optimizes an aggregate cost function…
A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
We study online competitive algorithms for the \emph{line chasing problem} in Euclidean spaces $\reals^d$, where the input consists of an initial point $P_0$ and a sequence of lines $X_1,X_2,...,X_m$, revealed one at a time. At each step…
This paper addresses the problem of optimal control of robotic sensing systems aimed at autonomous information gathering in scenarios such as environmental monitoring, search and rescue, and surveillance and reconnaissance. The information…
This research introduces a novel application of a masked Proximal Policy Optimization (PPO) algorithm from the field of deep reinforcement learning (RL), for determining the most efficient sequence of space debris visitation, utilizing the…
For a given polygonal region $P$, the Lawn Mowing Problem (LMP) asks for a shortest tour $T$ that gets within Euclidean distance 1 of every point in $P$; this is equivalent to computing a shortest tour for a unit-disk cutter $C$ that covers…
Given a set of points in the Euclidean space $\mathbb{R}^\ell$ with $\ell>1$, the pairwise distances between the points are determined by their spatial location and the metric $d$ that we endow $\mathbb{R}^\ell$ with. Hence, the distance…
As large language models (LLMs) see greater use in academic and commercial settings, there is increasing interest in methods that allow language models to generate texts aligned with human preferences. In this paper, we present an initial…
Papadimitriou and Yannakakis show that the polynomial-time solvability of a certain singleobjective problem determines the class of multiobjective optimization problems that admit a polynomial-time computable $(1+\varepsilon, \dots ,…
In inverse reinforcement learning (IRL), a learning agent infers a reward function encoding the underlying task using demonstrations from experts. However, many existing IRL techniques make the often unrealistic assumption that the agent…
We establish fundamental limits of tracking a moving target over the unit cube under the framework of 20 questions with measurement-dependent noise. In this problem, there is an oracle who knows the instantaneous location of a target. Our…
The Johnson-Lindenstrauss (JL) Lemma introduced the concept of dimension reduction via a random linear map, which has become a fundamental technique in many computational settings. For a set of $n$ points in $\mathbb{R}^d$ and any fixed…
Proximal Policy Optimization (PPO) is a widely used reinforcement learning algorithm known for its stability and sample efficiency, but it often suffers from premature convergence due to limited exploration. In this paper, we propose POEM…
Reinforcement Learning has drawn huge interest as a tool for solving optimal control problems. Solving a given problem (task or environment) involves converging towards an optimal policy. However, there might exist multiple optimal policies…