Related papers: Bounds for Algorithmic Mutual Information and a Un…
A learner aims to minimize a function $f$ by repeatedly querying a distributed oracle that provides noisy gradient evaluations. At the same time, the learner seeks to hide $\arg\min f$ from a malicious eavesdropper that observes the…
We try to establish a unified information theoretic approach to learning and to explore some of its applications. First, we define {\em predictive information} as the mutual information between the past and the future of a time series,…
We derive and analyze learning algorithms for apprenticeship learning, policy evaluation, and policy gradient for average reward criteria. Existing algorithms explicitly require an upper bound on the mixing time. In contrast, we build on…
We provide matching upper and lower bounds on the mutual information in noisy reconstruction of parity check codes and thereby prove a long-standing conjecture by Montanari [IEEE Transactions on Information Theory 2005]. Besides extending a…
We consider a time-varying first-order autoregressive model with irregular innovations, where we assume that the coefficient function is H\"{o}lder continuous. To estimate this function, we use a quasi-maximum likelihood based approach. A…
We develop an eigenspace estimation algorithm for distributed environments with arbitrary node failures, where a subset of computing nodes can return structurally valid but otherwise arbitrarily chosen responses. Notably, this setting…
We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…
Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution as compared to an offline optimum. On the other hand,…
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
We investigate so-called localisable information of bipartite states and a parallel notion of information deficit. Localisable information is defined as the amount of information that can be concentrated by means of classical communication…
Extracting meaning from uncertain, noisy data is a fundamental problem across time series analysis, pattern recognition, and language modeling. This survey presents a unified mathematical framework that connects classical estimation theory,…
Bilevel optimization and bilevel minimax optimization have recently emerged as unifying frameworks for a range of machine-learning tasks, including hyperparameter optimization and reinforcement learning. The existing literature focuses on…
We introduce the notions of algorithmic mutual information and rarity of quantum states. These definitions enjoy conservation inequalities over unitary transformations and partial traces. We show that a large majority of pure states have…
We present the results of detailed numerical study of a model for the sharing and sorting of informations in a community consisting of a large number of agents. The information gathering takes place in a sequence of mutual bipartite…
Markov Decision Processes are classically solved using Value Iteration and Policy Iteration algorithms. Recent interest in Reinforcement Learning has motivated the study of methods inspired by optimization, such as gradient ascent. Among…
We study the offline reinforcement learning (offline RL) problem, where the goal is to learn a reward-maximizing policy in an unknown Markov Decision Process (MDP) using the data coming from a policy $\mu$. In particular, we consider the…
We introduce a model of a randomly growing interface in multidimensional Euclidean space. The growth model incorporates a random order model as an ingredient of its graphical construction, in a way that replicates the connection between the…
We study the frontier between learnable and unlearnable hidden Markov models (HMMs). HMMs are flexible tools for clustering dependent data coming from unknown populations. The model parameters are known to be fully identifiable (up to…
The partially observable Markov decision process (POMDP) provides a principled general model for planning under uncertainty. However, solving a general POMDP is computationally intractable in the worst case. This paper introduces…
Standard Markov decision process (MDP) and reinforcement learning algorithms optimize the policy with respect to the expected gain. We propose an algorithm which enables to optimize an alternative objective: the probability that the gain is…