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arXiv research

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.

168,695 papers · 148 categories

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326395126 · Jun 202019922001200920172026
48 results for vanishing regret

Paper introduces a new GG^\star regret measure for online convex optimization with smooth losses.

problem Online convex optimization with smooth losses.
method Introduces a new GG^\star regret measure that depends on the cumulative squared gradient norm.
result The GG^\star regret can be arbitrarily sharper than existing measures when losses have vanishing curvature.

TVBO optimizes time-varying functions with asymptotically vanishing regret.

problem Understanding the asymptotic performance of TVBO for time-varying black-box functions.
method Provided upper and lower bounds for cumulative regret of TVBO algorithms.
result TVBO algorithms can achieve asymptotically vanishing regret under certain conditions.

In this paper, we formalise order-robust optimisation as an instance of online learning minimising simple regret, and propose Vroom, a zero'th order optimisation algorithm capable of achieving vanishing regret in non-stationary environments, while recovering favorable rates under stochastic reward-generating processes.…

2019-10-09abs ↗pdf ↗

New rule reduces exploration regret to logarithmic, improving bad episode handling.

problem Improving exploration regret in average reward MDPs.
method Replacing Doubling Trick with Vanishing Multiplicative rule in EVI-based algorithms.
result Regret is logarithmic under the new rule, significantly better than linear.

Bayesian optimization method for permutations accelerates combinatorial search.

problem Optimizing expensive-to-evaluate objectives on permutation problems.
method LAW2ORDER, a batch Bayesian optimization method based on the acquisition weighted kernel.
result LAW2ORDER achieves sublinear batch cumulative regret, demonstrating accelerated search.

The paper tackles robust policy learning from multiple data sources.

problem Learning a policy that generalizes across diverse settings from multiple heterogeneous data sources.
method Proposes a minimax regret optimization objective and a policy learning algorithm combining doubly robust offline policy evaluation and no-regret learning.
result Achieves minimal worst-case mixture regret up to a moderated vanishing rate of the total data across all sources.

No-regret optimization for time-varying functions using uncertainty injection.

problem Optimizing time-varying functions with no-regret in bandit feedback.
method W-SparQ-GP-UCB, incorporating uncertainty injection and additional queries.
result Achieves no-regret with a vanishing number of additional queries per iteration.

The problem of forecasting conditional probabilities of the next event given the past is considered in a general probabilistic setting. Given an arbitrary (large, uncountable) set C of predictors, we would like to construct a single predictor that performs asymptotically as well as the best predictor in C, on any data.…

2016-10-26abs ↗pdf ↗

This paper analyses the problem of Gaussian process (GP) bandits with deterministic observations. The analysis uses a branch and bound algorithm that is related to the UCB algorithm of (Srinivas et al., 2010). For GPs with Gaussian observation noise, with variance strictly greater than zero, (Srinivas et al., 2010) pro…

2012-03-09abs ↗pdf ↗

New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.

problem Adapting to an unknown margin parameter in batched nonparametric bandits.
method Introduces the regret inflation criterion and develops RoBIN algorithm to achieve optimal regret inflation.
result The optimal regret inflation grows polynomially with the horizon T, characterized by a convex optimization problem.

Gaussian prior and likelihood improve bandit learning performance.

problem Improving bandit learning with misspecified Gaussian distributions.
method An agent with a bounded information ratio interacts with a Bernoulli bandit based on a Gaussian prior and likelihood.
result The regret increase is at most linear in the square-root of the time horizon for diffuse distributions.

New algorithm reduces regret for kernelized bandits by adapting to specific problem instances.

problem Efficiently learning the optimizer of an unknown function in RKHS with noisy oracle.
method Instance-dependent regret analysis and a new minimax near-optimal algorithm.
result New algorithm achieves better performance on specific problem instances.

New algorithm identifies best arm in rested bandit setting.

problem Best arm identification in rested bandit with decreasing losses.
method Introduced a novel best arm identification problem and analyzed an arm elimination algorithm.
result Regret vanishes as time horizon increases, with convergence rate depending on expected loss function.

New algorithm robust to probabilistic unbounded adversarial attacks in bandit problems.

problem Powerful adversaries that can catastrophically perturb the revealed reward in bandit problems.
method Proposes med-E-UCB and med-εε-greedy algorithms based on sample median for robustness.
result Achieves O(logT)\mathcal{O}(\log T) pseudo-regret under arbitrary and unbounded reward perturbation.

LaMBO optimizes modular systems with switching costs, achieving better results than existing methods.

problem Optimizing systems with costly variable updates in a sequence of modules.
method Lazy Modular Bayesian Optimization (LaMBO) that minimizes switching costs.
result LaMBO achieves vanishing regret and improves over existing cost-aware Bayesian optimization algorithms.

Study on newsvendor problem with censored data, showing how much information is lost.

problem Minimizing costs in a newsvendor problem with limited historical demand data.
method Distributionally robust optimization framework, evaluating policies based on worst-case regret.
result Characterization of information loss due to demand censoring and development of a robust algorithm.

New model considers unfairness complaints to ensure multiple fairness criteria.

problem Ensuring fairness in systems that may conflict with each other.
method Data-driven model guided by unfairness complaints, supports multiple fairness criteria, and considers their incompatibilities. Stochastic and adversarial settings analyzed with efficient algorithms.
result Efficient algorithms for both stochastic and adversarial settings with competitive guarantees.

A new sequential method estimates Poisson means in streaming data, achieving optimality and efficiency.

problem Estimating Poisson means in a streaming, or online, framework.
method A quasi-Bayesian approach based on Newton's algorithm for a sequential estimate.
result Established frequentist guarantees including consistency and asymptotic optimality.

Regret minimization is treated as the golden rule in the traditional study of online learning. However, regret minimization algorithms tend to converge to the static optimum, thus being suboptimal for changing environments. To address this limitation, new performance measures, including dynamic regret and adaptive regr…

2020-02-06abs ↗pdf ↗

The paper analyzes the sliding regret of stochastic bandit algorithms.

problem Measuring the one-shot behavior of no-regret algorithms in stochastic bandits.
method Introducing sliding regret to measure the worst pseudo-regret over a time-window.
result Randomized methods have optimal sliding regret, while index policies have the worst possible sliding regret.

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/δ1/δ with probability δδ.

The notion of \emph{policy regret} in online learning is a well defined? performance measure for the common scenario of adaptive adversaries, which more traditional quantities such as external regret do not take into account. We revisit the notion of policy regret and first show that there are online learning settings …

2018-11-09abs ↗pdf ↗

Optimistic Hedge achieves optimal regret bounds in two-player zero-sum games.

problem Achieving optimal regret bounds for optimistic Hedge in two-player zero-sum games.
method Refined regret analysis and optimization problem formulation.
result Optimistic Hedge achieves O(logmlogn)O(\sqrt{\log m \log n}) regret bounds, matching upper and lower bounds.

We consider an online learning process to forecast a sequence of outcomes for nonconvex models. A typical measure to evaluate online learning algorithms is regret but such standard definition of regret is intractable for nonconvex models even in offline settings. Hence, gradient based definition of regrets are common f…

2018-11-13abs ↗pdf ↗

Optimal switching regret for all segmentations in online convex optimisation.

problem Non-stationary online convex optimisation problems.
method Developed an efficient algorithm to achieve optimal switching regret on every possible segmentation.
result Achieved asymptotically optimal switching regret on every possible segmentation simultaneously.

New approach for distributed online optimization of non-convex losses with sublinear regret.

problem Regret evaluation and consensus in distributed, multi-agent systems with non-convex losses.
method Composite regret metric and consensus-based online normalized gradient (CONGD) approach for pseudo-convex losses; offline optimization oracle for general non-convex losses.
result First sublinear regret bound for general distributed online non-convex learning.

Regret minimization is a powerful tool for solving large-scale problems; it was recently used in breakthrough results for large-scale extensive-form game solving. This was achieved by composing simplex regret minimizers into an overall regret-minimization framework for extensive-form game strategy spaces. In this paper…

2018-11-06abs ↗pdf ↗

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 TT with k<T2k < \frac{T}{2} zeros, the sequences of largest regret consist of alternating zeros and …

2019-06-21abs ↗pdf ↗

This paper considers the stability of online learning algorithms and its implications for learnability (bounded regret). We introduce a novel quantity called {\em forward regret} that intuitively measures how good an online learning algorithm is if it is allowed a one-step look-ahead into the future. We show that given…

2012-11-26abs ↗pdf ↗

Bandit algorithms struggle with consistent performance and robustness.

problem Achieving consistent and robust performance in stochastic multi-armed bandit settings.
method Analyzing regret minimization trade-offs and proposing distribution-oblivious algorithms.
result Logarithmic regret is inconsistent and super-logarithmic regret is necessary for consistent learning.