Related papers: Multiple Random Oracles Are Better Than One
The time-optimal $k$-server problem minimizes the time spent serving all requests instead of the distances traveled. We give a lower bound of $2k-1$ on the competitive ratio of any deterministic online algorithm for this problem, which…
We humans seem to have an innate understanding of the asymmetric progression of time, which we use to efficiently and safely perceive and manipulate our environment. Drawing inspiration from that, we address the problem of learning an arrow…
Historically, much of machine learning research has focused on the performance of the algorithm alone, but recently more attention has been focused on optimizing joint human-algorithm performance. Here, we analyze a specific type of…
We consider multi-task learning, which simultaneously learns related prediction tasks, to improve generalization performance. We factorize a coefficient matrix as the product of two matrices based on a low-rank assumption. These matrices…
As a step towards developing zero-shot task generalization capabilities in reinforcement learning (RL), we introduce a new RL problem where the agent should learn to execute sequences of instructions after learning useful skills that solve…
We consider Boolean functions f:{-1,1}^n->{-1,1} that are close to a sum of independent functions on mutually exclusive subsets of the variables. We prove that any such function is close to just a single function on a single subset. We also…
Q-Learning is a fundamental off-policy reinforcement learning (RL) algorithm that has the objective of approximating action-value functions in order to learn optimal policies. Nonetheless, it has difficulties in reconciling bias with…
We study the following distribution clustering problem: Given a hidden partition of $k$ distributions into two groups, such that the distributions within each group are the same, and the two distributions associated with the two clusters…
We investigate the approximability of several classes of real-valued functions by functions of a small number of variables ({\em juntas}). Our main results are tight bounds on the number of variables required to approximate a function…
Given i.i.d.~samples from an unknown distribution $P$, the goal of distribution learning is to recover the parameters of a distribution that is close to $P$. When $P$ belongs to the class of product distributions on the Boolean hypercube…
We consider the problem of testing distribution identity. Given a sequence of independent samples from an unknown distribution on a domain of size n, the goal is to check if the unknown distribution approximately equals a known distribution…
We study the problem of comparing ageing patterns of the lifetime of k-out-of-n systems. Mathematically, this reduces to being able to decide about a stochastic ordering relationship between different order statistics. We discuss such…
Consider a $k$-SAT formula $\Phi$ where every variable appears at most $d$ times. Let $\sigma$ be a satisfying assignment, sampled proportionally to $e^{\beta m(\sigma)}$ where $m(\sigma)$ is the number of true variables and $\beta$ is a…
We consider the problem of computing with many coins of unknown bias. We are given samples access to $n$ coins with \emph{unknown} biases $p_1,\dots, p_n$ and are asked to sample from a coin with bias $f(p_1, \dots, p_n)$ for a given…
We propose a quantum machine learning task that is provably easy for quantum computers and arguably hard for classical ones. The task involves predicting quantities of the form $\mathrm{Tr}[f(H)\rho]$, where $f$ is an unknown function,…
We consider the problem of learning from revealed preferences in an online setting. In our framework, each period a consumer buys an optimal bundle of goods from a merchant according to her (linear) utility function and current prices,…
We analyze the energy and training data requirements for supervised learning of an $M$-mode linear optical circuit by minimizing an empirical risk defined solely from the action of the circuit on coherent states. When the linear optical…
We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…
We give improved and almost optimal testers for several classes of Boolean functions on $n$ inputs that have concise representation in the uniform and distribution-free model. Classes, such as $k$-junta, $k$-linear functions, $s$-term DNF,…
We study the problem of learning a $n$-variables $k$-CNF formula $\Phi$ from its i.i.d. uniform random solutions, which is equivalent to learning a Boolean Markov random field (MRF) with $k$-wise hard constraints. Revisiting Valiant's…