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In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with continuous-time models and algorithms for several online…
Multi-objective combinatorial optimization seeks Pareto-optimal solutions over exponentially large discrete spaces, yet existing methods sacrifice generality, scalability, or theoretical guarantees. We reformulate it as an online learning…
In this paper, we consider an online optimization process, where the objective functions are not convex (nor concave) but instead belong to a broad class of continuous submodular functions. We first propose a variant of the Frank-Wolfe…
Recent literature on online learning has focused on developing adaptive algorithms that take advantage of a regularity of the sequence of observations, yet retain worst-case performance guarantees. A complementary direction is to develop…
We study the decades-old problem of online portfolio management and propose the first algorithm with logarithmic regret that is not based on Cover's Universal Portfolio algorithm and admits much faster implementation. Specifically Universal…
Deep reinforcement learning has achieved impressive successes yet often requires a very large amount of interaction data. This result is perhaps unsurprising, as using complicated function approximation often requires more data to fit, and…
We analyze the minimax regret of the adversarial bandit convex optimization problem. Focusing on the one-dimensional case, we prove that the minimax regret is $\widetilde\Theta(\sqrt{T})$ and partially resolve a decade-old open problem. Our…
We study online learning in constrained Markov decision processes (CMDPs) in which rewards and constraints may be either stochastic or adversarial. In such settings, Stradi et al.(2024) proposed the first best-of-both-worlds algorithm able…
In the contextual pricing problem a seller repeatedly obtains products described by an adversarially chosen feature vector in $\mathbb{R}^d$ and only observes the purchasing decisions of a buyer with a fixed but unknown linear valuation…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…
This paper considers online convex optimization with long term constraints, where constraints can be violated in intermediate rounds, but need to be satisfied in the long run. The cumulative constraint violation is used as the metric to…
In the problem of online portfolio selection as formulated by Cover (1991), the trader repeatedly distributes her capital over $ d $ assets in each of $ T > 1 $ rounds, with the goal of maximizing the total return. Cover proposed an…
We investigate online convex optimization in non-stationary environments and choose dynamic regret as the performance measure, defined as the difference between cumulative loss incurred by the online algorithm and that of any feasible…
Most bandit algorithm designs are purely theoretical. Therefore, they have strong regret guarantees, but also are often too conservative in practice. In this work, we pioneer the idea of algorithm design by minimizing the empirical Bayes…
Stochastic high dimensional bandit problems with low dimensional structures are useful in different applications such as online advertising and drug discovery. In this work, we propose a simple unified algorithm for such problems and…
This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each…
We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of…
We derive an alternative proof for the regret of Thompson sampling (\ts) in the stochastic linear bandit setting. While we obtain a regret bound of order $\widetilde{O}(d^{3/2}\sqrt{T})$ as in previous results, the proof sheds new light on…
This paper proposes a new family of algorithms for the online optimisation of composite objectives. The algorithms can be interpreted as the combination of the exponentiated gradient and $p$-norm algorithm. Combined with algorithmic ideas…
The principle of optimism in the face of uncertainty is prevalent throughout sequential decision making problems such as multi-armed bandits and reinforcement learning (RL). To be successful, an optimistic RL algorithm must over-estimate…