Contextual Search in the Presence of Adversarial Corruptions

Krishnamurthy, Akshay; Lykouris, Thodoris; Podimata, Chara; Schapire, Robert E.

doi:10.48550/arxiv.2002.11650

Cited by 3 publications

(3 citation statements)

References 15 publications

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“…Finally, a natural extension of the current framework would be to allow for the possibility of noisy feedback. It would be interesting to explore whether ideas developed for contextual search in Krishnamurthy et al (2020) to handle irrational agents could be used in the present context.…”

Section: Conclusion and Further Directionsmentioning

confidence: 99%

Contextual Inverse Optimization: Offline and Online Learning

Besbes¹,

Fonseca²,

Lobel³

2021

Preprint

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We study the problems of offline and online contextual optimization with feedback information, where instead of observing the loss, we observe, after-the-fact, the optimal action an oracle with full knowledge of the objective function would have taken. We aim to minimize regret, which is defined as the difference between our losses and the ones incurred by an all-knowing oracle. In the offline setting, the decision-maker has information available from past periods and needs to make one decision, while in the online setting, the decision-maker optimizes decisions dynamically over time based a new set of feasible actions and contextual functions in each period. For the offline setting, we characterize the optimal minimax policy, establishing the performance that can be achieved as a function of the underlying geometry of the information induced by the data. In the online setting, we leverage this geometric characterization to optimize the cumulative regret. We develop an algorithm that yields the first regret bound for this problem that is logarithmic in the time horizon.

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Section: Conclusion and Further Directionsmentioning

confidence: 99%

Contextual Inverse Optimization: Offline and Online Learning

Besbes¹,

Fonseca²,

Lobel³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Regret minimization on stochastic bandits with corruptions was first studied by Lykouris et al (2018), and has attracted extensive interest recently (Zimmert & Seldin, 2019;Li et al, 2019;Gupta et al, 2019;Lykouris et al, 2020;Liu & Lai, 2020;Krishnamurthy et al, 2020;Bogunovic et al, 2020). Pertaining to the BAI problem in the presence of corruptions, Altschuler et al (2019) studies a variation of the classical fixed-confidence setting and aims to find an item with a high median reward.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Sequential Shrinking: A Best Arm Identification Algorithm for Stochastic Bandits with Corruptions

Zhong,

Cheung,

Tan

2020

Preprint

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We consider a best arm identification (BAI) problem for stochastic bandits with adversarial corruptions in the fixed-budget setting of T steps. We design a novel randomized algorithm, PROBABILISTIC SEQUENTIAL SHRINKING(u) (PSS(u)), which is agnostic to the amount of corruptions. When the amount of corruptions per step (CPS) is below a threshold, PSS(u) identifies the best arm or item with probability tending to 1 as T → ∞. Otherwise, the optimality gap of the identified item degrades gracefully with the CPS. We argue that such a bifurcation is necessary. In addition, we show that when the CPS is sufficiently large, no algorithm can achieve a BAI probability tending to 1 as T → ∞. In PSS(u), the parameter u serves to balance between the optimality gap and success probability. En route, the injection of randomization is shown to be essential to mitigate the impact of corruptions. Indeed, we show that PSS(u) has a better performance than its deterministic analogue, the SUCCESSIVE HALVING (SH) algorithm by Karnin et al. (2013). PSS(2)'s performance guarantee matches SH's when there is no corruption. Finally, we identify a term in the exponent of the failure probability of PSS(u) that generalizes the common H 2 term for BAI under the fixed-budget setting.

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“…Some of the subsequent work studied dynamic pricing with limited supply, e.g., [8,9,5,52,6]. Departing from the stochastic version, [9,24] allow (several versions of) bounded change over time, and [17,37,36,34] allow arbitrary private values that are fully determined by the observable contexts.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Discretization for Adversarial Lipschitz Bandits

Podimata,

Slivkins

2020

Preprint

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Lipschitz bandits is a prominent version of multi-armed bandits that studies large, structured action spaces such as the [0, 1] interval, where similar actions are guaranteed to have similar rewards. A central theme here is the adaptive discretization of the action space, which gradually "zooms in" on the more promising regions thereof. The goal is to take advantage of "nicer" problem instances, while retaining near-optimal worst-case performance. While the stochastic version of the problem is well-understood, the general version with adversarially chosen rewards is not.We provide the first algorithm for adaptive discretization in the adversarial version, and derive instance-dependent regret bounds. In particular, we recover the worst-case optimal regret bound for the adversarial version, and the instance-dependent regret bound for the stochastic version. Further, an application of our algorithm to dynamic pricing (a version in which the algorithm repeatedly adjusts prices for a product) enjoys these regret bounds without any smoothness assumptions.

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Contextual Search in the Presence of Adversarial Corruptions

Cited by 3 publications

References 15 publications

Contextual Inverse Optimization: Offline and Online Learning

Contextual Inverse Optimization: Offline and Online Learning

Probabilistic Sequential Shrinking: A Best Arm Identification Algorithm for Stochastic Bandits with Corruptions

Adaptive Discretization for Adversarial Lipschitz Bandits

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