Related papers: Algorithmic Discrepancy Minimization
One of the prominent open problems in combinatorics is the discrepancy of set systems where each element lies in at most $t$ sets. The Beck-Fiala conjecture suggests that the right bound is $O(\sqrt{t})$, but for three decades the only…
Online prediction from experts is a fundamental problem in machine learning and several works have studied this problem under privacy constraints. We propose and analyze new algorithms for this problem that improve over the regret bounds of…
Increasingly, discrimination by algorithms is perceived as a societal and legal problem. As a response, a number of criteria for implementing algorithmic fairness in machine learning have been developed in the literature. This paper…
The information-theoretic analysis by Russo and Van Roy (2014) in combination with minimax duality has proved a powerful tool for the analysis of online learning algorithms in full and partial information settings. In most applications…
This paper establishes that optimistic algorithms attain gap-dependent and non-asymptotic logarithmic regret for episodic MDPs. In contrast to prior work, our bounds do not suffer a dependence on diameter-like quantities or ergodicity, and…
Here, we provide a supplementary material for Takayuki Osogami, "Uncorrected least-squares temporal difference with lambda-return," which appears in {\it Proceedings of the 34th AAAI Conference on Artificial Intelligence} (AAAI-20).
Many problems in computer science and applied mathematics require rounding a vector $\mathbf{w}$ of fractional values lying in the interval $[0,1]$ to a binary vector $\mathbf{x}$ so that, for a given matrix $\mathbf{A}$,…
We study learning algorithms when there is a mismatch between the distributions of the training and test datasets of a learning algorithm. The effect of this mismatch on the generalization error and model misspecification are quantified.…
Consistency is the theoretical property of a meta learning algorithm that ensures that, under certain assumptions, it can adapt to any task at test time. An open question is whether and how theoretical consistency translates into practice,…
In recent years, there has been an increasing awareness of both the public and scientific community that algorithmic systems can reproduce, amplify, or even introduce unfairness in our societies. These lecture notes provide an introduction…
The law of the iterated logarithm for discrepancies of geometric progressions with small ratios is proved.
Simulation-based verification algorithms can provide formal safety guarantees for nonlinear and hybrid systems. The previous algorithms rely on user provided model annotations called discrepancy function, which are crucial for computing…
We study the convergence behavior of the celebrated temporal-difference (TD) learning algorithm. By looking at the algorithm through the lens of optimization, we first argue that TD can be viewed as an iterative optimization algorithm where…
Algorithmic meta-theorems are general algorithmic results applying to a whole range of problems, rather than just to a single problem alone. They often have a "logical" and a "structural" component, that is they are results of the form:…
In this paper, we introduce a novel family of iterative algorithms which carry out $\alpha$-divergence minimisation in a Variational Inference context. They do so by ensuring a systematic decrease at each step in the $\alpha$-divergence…
In this paper, we study the problem of recovering the latent vertex correspondence between two correlated random graphs with vastly inhomogeneous and unknown edge probabilities between different pairs of vertices. Inspired by and extending…
Combining measurements which have "theoretical uncertainties" is a delicate matter, due to an unclear statistical basis. We present an algorithm based on the notion that a theoretical uncertainty represents an estimate of bias.
Motivated by the celebrated Beck-Fiala conjecture, we consider the random setting where there are $n$ elements and $m$ sets and each element lies in $t$ randomly chosen sets. In this setting, Ezra and Lovett showed an $O((t \log t)^{1/2})$…
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and…
We study reinforcement learning for episodic Markov Decision Processes (MDPs) whose transitions are modelled by a multinomial logistic (MNL) model. Existing algorithms for MNL mixture MDPs yield a regret of $\smash{\tilde{O}(dH^2\sqrt{T})}$…