A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
This paper analyzes regret bounds for Gaussian process Thompson sampling.
problem Analyzing the performance of Gaussian process Thompson sampling (GP-TS) in Bayesian optimization.
method The paper derives several regret bounds for GP-TS, including a lower bound, upper bounds on the second moment of cumulative regret, expected lenient regret, and improved cumulative regret.
result The paper provides improved regret upper bounds for GP-TS, showing that it suffers from a polynomial dependence on 1/δ with probability δ.
We study the Thompson sampling algorithm in an adversarial setting, specifically, for adversarial bit prediction. We characterize the bit sequences with the smallest and largest expected regret. Among sequences of length T with k<2T zeros, the sequences of largest regret consist of alternating zeros and …
We revisit the challenge of designing online algorithms for the bandit convex optimization problem (BCO) which are also scalable to high dimensional problems. Hence, we consider algorithms that are \textit{projection-free}, i.e., based on the conditional gradient method whose only access to the feasible decision set, i…
We consider a multiobjective multiarmed bandit problem with lexicographically ordered objectives. In this problem, the goal of the learner is to select arms that are lexicographic optimal as much as possible without knowing the arm reward distributions beforehand. We capture this goal by defining a multidimensional for…
We prove non-asymptotic lower bounds on the expectation of the maximum of d independent Gaussian variables and the expectation of the maximum of d independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (…
Learning reward functions can lead to poor policy performance despite low error.
problem Low error in learned reward functions does not guarantee low regret in policy performance.
method Mathematical analysis of reward learning and policy optimization.
result A low expected test error of the reward model guarantees low worst-case regret, but error-regret mismatch can occur with certain data distributions.
Optimal learning rate schedules for SGD in changing data distributions.
problem Minimizing regret in online learning with changing data distributions.
method Characterized optimal schedules for linear regression, proposed schedules for general convex and non-convex losses, and defined a notion of regret for non-convex losses.
result Upper and lower bounds for regret with constants for convex losses, and an upper bound on total expected regret for non-convex losses.
We consider a setting where an agent's uncertainty is represented by a set of probability measures, rather than a single measure. Measure-bymeasure updating of such a set of measures upon acquiring new information is well-known to suffer from problems; agents are not always able to learn appropriately. To deal with the…
We study the regret of optimal strategies for online convex optimization games. Using von Neumann's minimax theorem, we show that the optimal regret in this adversarial setting is closely related to the behavior of the empirical minimization algorithm in a stochastic process setting: it is equal to the maximum, over jo…
The paper addresses frequentist regret of Linear Thompson Sampling in stochastic linear bandits.
problem The frequentist regret of Linear Thompson Sampling (LinTS) is worse than its Bayesian counterpart.
method The paper proves the fundamental nature of the frequentist regret bound for LinTS and proposes a data-driven version of LinTS to achieve minimax optimal frequentist regret.
result The frequentist regret bound for LinTS is O(ddT), which is the best possible under certain conditions.
We consider the problem of learning in single-player and multiplayer multiarmed bandit models. Bandit problems are classes of online learning problems that capture exploration versus exploitation tradeoffs. In a multiarmed bandit model, players can pick among many arms, and each play of an arm generates an i.i.d. rewar…
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 all…
We study contextual bandits with budget and time constraints, referred to as constrained contextual bandits.The time and budget constraints significantly complicate the exploration and exploitation tradeoff because they introduce complex coupling among contexts over time.Such coupling effects make it difficult to obtai…
We consider stochastic multi-armed bandits where the expected reward is a unimodal function over partially ordered arms. This important class of problems has been recently investigated in (Cope 2009, Yu 2011). The set of arms is either discrete, in which case arms correspond to the vertices of a finite graph whose stru…
We study the dynamic assortment planning problem, where for each arriving customer, the seller offers an assortment of substitutable products and customer makes the purchase among offered products according to an uncapacitated multinomial logit (MNL) model. Since all the utility parameters of MNL are unknown, the selle…