Related papers: Unconstrained Online Linear Learning in Hilbert Sp…
We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm,…
Regret minimization is a general approach to online optimization which plays a crucial role in many algorithms for approximating Nash equilibria in two-player zero-sum games. The literature mainly focuses on solving individual games in…
We introduce an online convex optimization algorithm which utilizes projected subgradient descent with optimal adaptive learning rates. Our method provides second-order minimax-optimal dynamic regret guarantee (i.e. dependent on the sum of…
We consider the fundamental problem of prediction with expert advice where the experts are "optimizable": there is a black-box optimization oracle that can be used to compute, in constant time, the leading expert in retrospect at any point…
Regret minimization has proved to be a versatile tool for tree-form sequential decision making and extensive-form games. In large two-player zero-sum imperfect-information games, modern extensions of counterfactual regret minimization (CFR)…
We study the model-based undiscounted reinforcement learning for partially observable Markov decision processes (POMDPs). The oracle we consider is the optimal policy of the POMDP with a known environment in terms of the average reward over…
The regret bound of dynamic online learning algorithms is often expressed in terms of the variation in the function sequence ($V_T$) and/or the path-length of the minimizer sequence after $T$ rounds. For strongly convex and smooth…
We study online convex optimization with constraints consisting of multiple functional constraints and a relatively simple constraint set, such as a Euclidean ball. As enforcing the constraints at each time step through projections is…
We study the problem of online convex optimization (OCO) under unknown linear constraints that are either static, or stochastically time-varying. For this problem, we introduce an algorithm that we term Optimistically Safe OCO (OSOCO) and…
We study the online calibration of multi-dimensional forecasts over an arbitrary convex set $\mathcal{P} \subset \mathbb{R}^d$ relative to an arbitrary norm $\Vert\cdot\Vert$. We connect this with the problem of external regret minimization…
This paper considers online convex optimization over a complicated constraint set, which typically consists of multiple functional constraints and a set constraint. The conventional online projection algorithm (Zinkevich, 2003) can be…
This work studies the problem of sequential control in an unknown, nonlinear dynamical system, where we model the underlying system dynamics as an unknown function in a known Reproducing Kernel Hilbert Space. This framework yields a general…
We study a new class of online learning problems where each of the online algorithm's actions is assigned an adversarial value, and the loss of the algorithm at each step is a known and deterministic function of the values assigned to its…
We provide the first algorithm for online bandit linear optimization whose regret after T rounds is of order sqrt{Td ln N} on any finite class X of N actions in d dimensions, and of order d*sqrt{T} (up to log factors) when X is infinite.…
In online convex optimization, some efficient algorithms have been designed for each of the individual classes of objective functions, e.g., convex, strongly convex, and exp-concave. However, existing regret analyses, including those of…
We study online prediction where regret of the algorithm is measured against a benchmark defined via evolving constraints. This framework captures online prediction on graphs, as well as other prediction problems with combinatorial…
We study the problem of online learning with a notion of regret defined with respect to a set of strategies. We develop tools for analyzing the minimax rates and for deriving regret-minimization algorithms in this scenario. While the…
We study Online Convex Optimization in the unbounded setting where neither predictions nor gradient are constrained. The goal is to simultaneously adapt to both the sequence of gradients and the comparator. We first develop parameter-free…
We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$. For $L$-smooth convex loss, we provide…
In game-theoretic learning, several agents are simultaneously following their individual interests, so the environment is non-stationary from each player's perspective. In this context, the performance of a learning algorithm is often…