arXiv subjects

Viktor Bengs

Publications and source records attributed to Viktor Bengs.

29 records · Page 2Linked to original sources

arXiv2022

Finding Optimal Arms in Non-stochastic Combinatorial Bandits with Semi-bandit Feedback and Finite Budget

We consider the combinatorial bandits problem with semi-bandit feedback under finite sampling budget constraints, in which the learner can carry out its action only for a limited number of times specified by an overall budget. The action is to choose a set of arms, whereupon feedback for each arm in the chosen set is received. Unlike existing works, we study this problem in a non-stochastic setting with subset-dependent feedback, i.e., the semi-bandit feedback received could be generated by an oblivious adversary and also might depend on the chosen set of arms. In addition, we consider a general feedback scenario covering both the numerical-based as well as preference-based case and introduce a sound theoretical framework for this setting guaranteeing sensible notions of optimal arms, which a learner seeks to find. We suggest a generic algorithm suitable to cover the full spectrum of conceivable arm elimination strategies from aggressive to conservative. Theoretical questions about the sufficient and necessary budget of the algorithm to find the best arm are answered and complemented by deriving lower bounds for any learning algorithm for this problem scenario.

cs.LG↗

arXiv2022

Stochastic Contextual Dueling Bandits under Linear Stochastic Transitivity Models

We consider the regret minimization task in a dueling bandits problem with context information. In every round of the sequential decision problem, the learner makes a context-dependent selection of two choice alternatives (arms) to be compared with each other and receives feedback in the form of noisy preference information. We assume that the feedback process is determined by a linear stochastic transitivity model with contextualized utilities (CoLST), and the learner's task is to include the best arm (with highest latent context-dependent utility) in the duel. We propose a computationally efficient algorithm, $\texttt{CoLSTIM}$, which makes its choice based on imitating the feedback process using perturbed context-dependent utility estimates of the underlying CoLST model. If each arm is associated with a $d$-dimensional feature vector, we show that $\texttt{CoLSTIM}$ achieves a regret of order $\tilde O( \sqrt{dT})$ after $T$ learning rounds. Additionally, we also establish the optimality of $\texttt{CoLSTIM}$ by showing a lower bound for the weak regret that refines the existing average regret analysis. Our experiments demonstrate its superiority over state-of-art algorithms for special cases of CoLST models.

cs.LG↗

arXiv2022

Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.

cs.LG↗

arXiv2022

A Survey of Methods for Automated Algorithm Configuration

Algorithm configuration (AC) is concerned with the automated search of the most suitable parameter configuration of a parametrized algorithm. There is currently a wide variety of AC problem variants and methods proposed in the literature. Existing reviews do not take into account all derivatives of the AC problem, nor do they offer a complete classification scheme. To this end, we introduce taxonomies to describe the AC problem and features of configuration methods, respectively. We review existing AC literature within the lens of our taxonomies, outline relevant design choices of configuration approaches, contrast methods and problem variants against each other, and describe the state of AC in industry. Finally, our review provides researchers and practitioners with a look at future research directions in the field of AC.

cs.AI↗

arXiv2022

Non-Stationary Dueling Bandits

We study the non-stationary dueling bandits problem with $K$ arms, where the time horizon $T$ consists of $M$ stationary segments, each of which is associated with its own preference matrix. The learner repeatedly selects a pair of arms and observes a binary preference between them as feedback. To minimize the accumulated regret, the learner needs to pick the Condorcet winner of each stationary segment as often as possible, despite preference matrices and segment lengths being unknown. We propose the $\mathrm{Beat\, the\, Winner\, Reset}$ algorithm and prove a bound on its expected binary weak regret in the stationary case, which tightens the bound of current state-of-art algorithms. We also show a regret bound for the non-stationary case, without requiring knowledge of $M$ or $T$. We further propose and analyze two meta-algorithms, $\mathrm{DETECT}$ for weak regret and $\mathrm{Monitored\, Dueling\, Bandits}$ for strong regret, both based on a detection-window approach that can incorporate any dueling bandit algorithm as a black-box algorithm. Finally, we prove a worst-case lower bound for expected weak regret in the non-stationary case.

cs.LG↗

arXiv2021

Preselection Bandits

In this paper, we introduce the Preselection Bandit problem, in which the learner preselects a subset of arms (choice alternatives) for a user, which then chooses the final arm from this subset. The learner is not aware of the user's preferences, but can learn them from observed choices. In our concrete setting, we allow these choices to be stochastic and model the user's actions by means of the Plackett-Luce model. The learner's main task is to preselect subsets that eventually lead to highly preferred choices. To formalize this goal, we introduce a reasonable notion of regret and derive lower bounds on the expected regret. Moreover, we propose algorithms for which the upper bound on expected regret matches the lower bound up to a logarithmic term of the time horizon.

cs.LG↗

arXiv2021

Machine Learning for Online Algorithm Selection under Censored Feedback

In online algorithm selection (OAS), instances of an algorithmic problem class are presented to an agent one after another, and the agent has to quickly select a presumably best algorithm from a fixed set of candidate algorithms. For decision problems such as satisfiability (SAT), quality typically refers to the algorithm's runtime. As the latter is known to exhibit a heavy-tail distribution, an algorithm is normally stopped when exceeding a predefined upper time limit. As a consequence, machine learning methods used to optimize an algorithm selection strategy in a data-driven manner need to deal with right-censored samples, a problem that has received little attention in the literature so far. In this work, we revisit multi-armed bandit algorithms for OAS and discuss their capability of dealing with the problem. Moreover, we adapt them towards runtime-oriented losses, allowing for partially censored data while keeping a space- and time-complexity independent of the time horizon. In an extensive experimental evaluation on an adapted version of the ASlib benchmark, we demonstrate that theoretically well-founded methods based on Thompson sampling perform specifically strong and improve in comparison to existing methods.

cs.LG↗

arXiv2021

Preference-based Online Learning with Dueling Bandits: A Survey

In machine learning, the notion of multi-armed bandits refers to a class of online learning problems, in which an agent is supposed to simultaneously explore and exploit a given set of choice alternatives in the course of a sequential decision process. In the standard setting, the agent learns from stochastic feedback in the form of real-valued rewards. In many applications, however, numerical reward signals are not readily available -- instead, only weaker information is provided, in particular relative preferences in the form of qualitative comparisons between pairs of alternatives. This observation has motivated the study of variants of the multi-armed bandit problem, in which more general representations are used both for the type of feedback to learn from and the target of prediction. The aim of this paper is to provide a survey of the state of the art in this field, referred to as preference-based multi-armed bandits or dueling bandits. To this end, we provide an overview of problems that have been considered in the literature as well as methods for tackling them. Our taxonomy is mainly based on the assumptions made by these methods about the data-generating process and, related to this, the properties of the preference-based feedback.

cs.LG↗

arXiv2020

Online Preselection with Context Information under the Plackett-Luce Model

We consider an extension of the contextual multi-armed bandit problem, in which, instead of selecting a single alternative (arm), a learner is supposed to make a preselection in the form of a subset of alternatives. More specifically, in each iteration, the learner is presented a set of arms and a context, both described in terms of feature vectors. The task of the learner is to preselect $k$ of these arms, among which a final choice is made in a second step. In our setup, we assume that each arm has a latent (context-dependent) utility, and that feedback on a preselection is produced according to a Plackett-Luce model. We propose the CPPL algorithm, which is inspired by the well-known UCB algorithm, and evaluate this algorithm on synthetic and real data. In particular, we consider an online algorithm selection scenario, which served as a main motivation of our problem setting. Here, an instance (which defines the context) from a certain problem class (such as SAT) can be solved by different algorithms (the arms), but only $k$ of these algorithms can actually be run.

cs.LG↗

arXiv2019

Uniform approximation in classical weak convergence theory

A common statistical task lies in showing asymptotic normality of certain statistics. In many of these situations, classical textbook results on weak convergence theory suffice for the problem at hand. However, there are quite some scenarios where stronger results are needed in order to establish an asymptotic normal approximation uniformly over a family of probability measures. In this note we collect some results in this direction. We restrict ourselves to weak convergence in $\mathbb R^d$ with continuous limit measures.

math.PR↗

arXiv2019

Asymptotic confidence sets for the jump curve in bivariate regression problems

We construct uniform and point-wise asymptotic confidence sets for the single edge in an otherwise smooth image function which are based on rotated differences of two one-sided kernel estimators. Using methods from M-estimation, we show consistency of the estimators of location, slope and height of the edge function and develop a uniform linearization of the contrast process. The uniform confidence bands then rely on a Gaussian approximation of the score process together with anti-concentration results for suprema of Gaussian processes, while point-wise bands are based on asymptotic normality. The finite-sample performance of the point-wise proposed methods is investigated in a simulation study. An illustration to real-world image processing is also given.

math.ST↗