Asymptotically optimal algorithm
View article: Bang-Bang Evasion: Its Stochastic Optimality and a Terminal-Set-Based Implementation
Bang-Bang Evasion: Its Stochastic Optimality and a Terminal-Set-Based Implementation Open
We address the problem of optimal evasion in a planar endgame engagement, where a target with bounded lateral acceleration seeks to avoid interception by a missile guided by a linear feedback law. Contrary to existing approaches, that assu…
View article: An exact method for a problem of time slot pricing
An exact method for a problem of time slot pricing Open
A company provides a service at different time slots, each slot being endowed with a capacity. A non-atomic population of users is willing to purchase this service. The population is modeled as a continuous measure over the preferred times…
View article: Ramanujan-like Expansion in Random Regular Graphs: A Threshold Phenomenon
Ramanujan-like Expansion in Random Regular Graphs: A Threshold Phenomenon Open
This paper investigates the emergence of Ramanujan-like expansion properties in random regular graphs (RRGs), focusing on the existence and characteristics of a threshold phenomenon. Ramanujan graphs are optimal expanders whose spectral ga…
View article: Modified Equations for Stochastic Optimization
Modified Equations for Stochastic Optimization Open
In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prov…
View article: Modified Equations for Stochastic Optimization
Modified Equations for Stochastic Optimization Open
In this thesis, we extend the recently introduced theory of stochastic modified equations (SMEs) for stochastic gradient optimization algorithms. In Ch. 3 we study time-inhomogeneous SDEs driven by Brownian motion. For certain SDEs we prov…
View article: Expected Complexity of Barcode Reduction
Expected Complexity of Barcode Reduction Open
We study the algorithmic complexity of computing the persistence barcode of a randomly generated filtration. We provide a general technique to bound the expected complexity of reducing the boundary matrix in terms of the density of its red…
View article: Ramanujan-like Expansion in Random Regular Graphs: A Threshold Phenomenon
Ramanujan-like Expansion in Random Regular Graphs: A Threshold Phenomenon Open
This paper investigates the emergence of Ramanujan-like expansion properties in random regular graphs (RRGs), focusing on the existence and characteristics of a threshold phenomenon. Ramanujan graphs are optimal expanders whose spectral ga…
View article: Trinity Theorem for Windowed Measurement\\[10pt]\large Born = Information Projection (iff),\\Pointer = Spectral Minimum (iff),\\Windows = Minimax Optimal
Trinity Theorem for Windowed Measurement\\[10pt]\large Born = Information Projection (iff),\\Pointer = Spectral Minimum (iff),\\Windows = Minimax Optimal Open
Under unified framework of de Branges--Kreĭn (DBK) canonical system, scattering--functional equation dictionary and Bregman/information geometry, this paper establishes ``Trinity Theorem'' for windowed measurement. Conclusions in three tie…
View article: Geometry-Based Bounds on the Capacity of Peak-Limited and Band-Limited Signals over the Additive White Gaussian Noise Channel at a High SNR
Geometry-Based Bounds on the Capacity of Peak-Limited and Band-Limited Signals over the Additive White Gaussian Noise Channel at a High SNR Open
We present a new computable geometry-based upper bound on the capacity of peak-power-limited and band-limited signal over the Additive White Gaussian Noise Channel. The peak limit applies at continuous time. The bound is a function of the …
View article: Trinity Theorem for Windowed Measurement\\[10pt]\large Born = Information Projection (iff),\\Pointer = Spectral Minimum (iff),\\Windows = Minimax Optimal
Trinity Theorem for Windowed Measurement\\[10pt]\large Born = Information Projection (iff),\\Pointer = Spectral Minimum (iff),\\Windows = Minimax Optimal Open
Under unified framework of de Branges--Kreĭn (DBK) canonical system, scattering--functional equation dictionary and Bregman/information geometry, this paper establishes ``Trinity Theorem'' for windowed measurement. Conclusions in three tie…
View article: An asymptotically exact multiple testing procedure under dependence
An asymptotically exact multiple testing procedure under dependence Open
View article: Quantitative Frameproof Codes and Hypergraphs
Quantitative Frameproof Codes and Hypergraphs Open
Frameproof codes are a class of secure codes introduced by Boneh and Shaw in the context of digital fingerprinting, and have been widely studied from a combinatorial point of view. In this paper, we study a quantitative extension of framep…
View article: Quantitative Frameproof Codes and Hypergraphs
Quantitative Frameproof Codes and Hypergraphs Open
Frameproof codes are a class of secure codes introduced by Boneh and Shaw in the context of digital fingerprinting, and have been widely studied from a combinatorial point of view. In this paper, we study a quantitative extension of framep…
View article: A Fast Binary Splitting Approach for Non-Adaptive Learning of Erdős--Rényi Graphs
A Fast Binary Splitting Approach for Non-Adaptive Learning of Erdős--Rényi Graphs Open
We study the problem of learning an unknown graph via group queries on node subsets, where each query reports whether at least one edge is present among the queried nodes. In general, learning arbitrary graphs with $n$ nodes and $k$ edges …
View article: The Star Product of Uniformly Random Codes
The Star Product of Uniformly Random Codes Open
We consider the problem of determining the expected dimension of the star product of two uniformly random linear codes that are not necessarily of the same dimension. We achieve this by establishing a correspondence between the star produc…
View article: Fast Decoding for Non-Adaptive Learning of Erdős--Rényi Random Graphs
Fast Decoding for Non-Adaptive Learning of Erdős--Rényi Random Graphs Open
We study the problem of learning an unknown graph via group queries on node subsets, where each query reports whether at least one edge is present among the queried nodes. In general, learning arbitrary graphs with \(n\) nodes and \(k\) ed…
View article: The Star Product of Uniformly Random Codes
The Star Product of Uniformly Random Codes Open
We consider the problem of determining the expected dimension of the star product of two uniformly random linear codes that are not necessarily of the same dimension. We achieve this by establishing a correspondence between the star produc…
View article: Robustness of Online Inventory Balancing to Inventory Shocks
Robustness of Online Inventory Balancing to Inventory Shocks Open
In classic adversarial online resource allocation problems such as AdWords, customers arrive online while products are given offline with a fixed initial inventory. To ensure revenue guarantees under uncertainty, the decision maker must ba…
View article: Robustness of Online Inventory Balancing to Inventory Shocks
Robustness of Online Inventory Balancing to Inventory Shocks Open
In classic adversarial online resource allocation problems such as AdWords, customers arrive online while products are given offline with a fixed initial inventory. To ensure revenue guarantees under uncertainty, the decision maker must ba…
View article: Learning-Augmented Online Algorithms for Nonclairvoyant Joint Replenishment Problem with Deadlines
Learning-Augmented Online Algorithms for Nonclairvoyant Joint Replenishment Problem with Deadlines Open
This paper considers using predictions in the context of the online Joint Replenishment Problem with Deadlines (JRP-D). Prior work includes asymptotically optimal competitive ratios of $O(1)$ for the clairvoyant setting and $O(\sqrt{n})$ o…
View article: Learning-Augmented Online Algorithms for Nonclairvoyant Joint Replenishment Problem with Deadlines
Learning-Augmented Online Algorithms for Nonclairvoyant Joint Replenishment Problem with Deadlines Open
This paper considers using predictions in the context of the online Joint Replenishment Problem with Deadlines (JRP-D). Prior work includes asymptotically optimal competitive ratios of $O(1)$ for the clairvoyant setting and $O(\sqrt{n})$ o…
View article: The Rate-Distortion-Perception Trade-Off with Algorithmic Realism
The Rate-Distortion-Perception Trade-Off with Algorithmic Realism Open
Realism constraints (or constraints on perceptual quality) have received considerable recent attention within the context of lossy compression, particularly of images. Theoretical studies of lossy compression indicate that high-rate common…
View article: The Rate-Distortion-Perception Trade-Off with Algorithmic Realism
The Rate-Distortion-Perception Trade-Off with Algorithmic Realism Open
Realism constraints (or constraints on perceptual quality) have received considerable recent attention within the context of lossy compression, particularly of images. Theoretical studies of lossy compression indicate that high-rate common…
View article: Asymptotically optimal approximate Hadamard matrices
Asymptotically optimal approximate Hadamard matrices Open
In this paper, we study approximate Hadamard matrices, that is, well-conditioned $n\times n$ matrices with all entries in $\{\pm1\}$. We show that the smallest-possible condition number goes to $1$ as $n\to\infty$, and we identify some exp…
View article: A graph-informed regret metric for optimal distributed control
A graph-informed regret metric for optimal distributed control Open
We consider the optimal control of large-scale systems using distributed controllers with a network topology that mirrors the coupling graph between subsystems. In this work, we introduce spatial regret, a graph-informed metric that measur…
View article: An Online Multiobjective Policy Gradient for Long-run Average-reward Markov Decision Process
An Online Multiobjective Policy Gradient for Long-run Average-reward Markov Decision Process Open
We propose a reinforcement learning (RL) framework for multi-objective decision-making, where the agent seeks to optimize a vector of rewards rather than a single scalar value. The objective is to ensure that the time-averaged reward vecto…
View article: An Online Multiobjective Policy Gradient for Long-run Average-reward Markov Decision Process
An Online Multiobjective Policy Gradient for Long-run Average-reward Markov Decision Process Open
We propose a reinforcement learning (RL) framework for multi-objective decision-making, where the agent seeks to optimize a vector of rewards rather than a single scalar value. The objective is to ensure that the time-averaged reward vecto…
View article: Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm
Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm Open
The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important statist…
View article: Rigorous Methods for Computational Number Theory
Rigorous Methods for Computational Number Theory Open
We present the first algorithm for computing class groups and unit groups of arbitrary number fields that provably runs in probabilistic subexponential time, assuming the Extended Riemann Hypothesis (ERH). Previous subexponential algorithm…
View article: Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm
Autocovariance and Optimal Design for Random Walk Metropolis-Hastings Algorithm Open
The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important statist…