相关论文: Orlicz regrets to consistently bound statistics of…

Environmental variables that fluctuate randomly and dynamically over time, such as water quality indices, are considered to be stochastic. They exhibit sub-exponential memory structures that should be accounted for in their modeling and…

The regret bound of an optimization algorithms is one of the basic criteria for evaluating the performance of the given algorithm. By inspecting the differences between the regret bounds of traditional algorithms and adaptive one, we…

The need for fast and robust optimization algorithms are of critical importance in all areas of machine learning. This paper treats the task of designing optimization algorithms as an optimal control problem. Using regret as a metric for an…

We study finite episodic Markov decision processes incorporating dynamic risk measures to capture risk sensitivity. To this end, we present two model-based algorithms applied to \emph{Lipschitz} dynamic risk measures, a wide range of risk…

The performance of online convex optimization algorithms in a dynamic environment is often expressed in terms of the dynamic regret, which measures the decision maker's performance against a sequence of time-varying comparators. In the…

In this paper, we address tracking of a time-varying parameter with unknown dynamics. We formalize the problem as an instance of online optimization in a dynamic setting. Using online gradient descent, we propose a method that sequentially…

Optimization in the presence of sharp (non-Lipschitz), unpredictable (w.r.t. time and amount) changes is a challenging and largely unexplored problem of great significance. We consider the class of piecewise Lipschitz functions, which is…

This paper is motivated by recent research in the $d$-dimensional stochastic linear bandit literature, which has revealed an unsettling discrepancy: algorithms like Thompson sampling and Greedy demonstrate promising empirical performance,…

This work introduces the first small-loss and gradual-variation regret bounds for online portfolio selection, marking the first instances of data-dependent bounds for online convex optimization with non-Lipschitz, non-smooth losses. The…

This guide provides a reference for high-probability regret bounds in empirical risk minimization (ERM). The presentation is modular: we begin with intuition and general proof strategies, then state broadly applicable guarantees under…

A natural goal when designing online learning algorithms for non-stationary environments is to bound the regret of the algorithm in terms of the temporal variation of the input sequence. Intuitively, when the variation is small, it should…

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic…

We propose a novel approach for analyzing dynamic regret of first-order constrained online convex optimization algorithms for strongly convex and Lipschitz-smooth objectives. Crucially, we provide a general analysis that is applicable to a…

Statistical performance bounds for reinforcement learning (RL) algorithms can be critical for high-stakes applications like healthcare. This paper introduces a new framework for theoretically measuring the performance of such algorithms…

In this work, we consider a sequence of stochastic optimization problems following a time-varying distribution via the lens of online optimization. Assuming that the loss function satisfies the Polyak-{\L}ojasiewicz condition, we apply…

We consider the classical problem of sequential resource allocation where a decision maker must repeatedly divide a budget between several resources, each with diminishing returns. This can be recast as a specific stochastic optimization…

In online convex optimization (OCO), Lipschitz continuity of the functions is commonly assumed in order to obtain sublinear regret. Moreover, many algorithms have only logarithmic regret when these functions are also strongly convex.…

A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the…

Risk measures connect probability theory or statistics to optimization, particularly to convex optimization. They are nowadays standard in applications of finance and in insurance involving risk aversion. This paper investigates a wide…

We study the dynamic regret of multi-armed bandit and experts problem in non-stationary stochastic environments. We introduce a new parameter $\Lambda$, which measures the total statistical variance of the loss distributions over $T$ rounds…