7 papers
Generalizing Markowitz Portfolio Optimization by a Quadratic Risk Measure
Ignas Gasparavičius, Andrius Grigutis
We show that the key optimization results of the classical Markowitz portfolio selection theory, originally formulated for variance as the risk measure, remain available in explici…
Sharp Optimal Algorithm for Derivative-Free Stochastic Convex Optimization in One Dimension
Alexandra Carpentier, Chloé Rouyer, Alexandre Tsybakov +1
Stochastic convex optimization is a classical problem with well-understood guarantees under first-order feedback. In contrast, for zero-order optimization with noisy function evalu…
Gradient-free stochastic optimization of derivatives under strong convexity
Arya Akhavan, Sirine Louati, Alexandre B. Tsybakov
We consider the problem of minimizing the -th order partial derivative of an unknown function along a fixed coordinate direction , based on noisy queri…
Gradient-free stochastic optimization for additive models
Arya Akhavan, Alexandre B. Tsybakov
We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-Łojasiewicz or the strong convexity condition. Additionall…
Minimax estimation of functionals in sparse vector model with correlated observations
Yuhao Wang, Pengkun Yang, Alexandre B. Tsybakov
We consider the observations of an unknown -sparse vector corrupted by Gaussian noise with zero mean and unknown covariance matrix . We propos…
A conversion theorem and minimax optimality for continuum contextual bandits
Arya Akhavan, Karim Lounici, Massimiliano Pontil +1
We study the contextual continuum bandits problem, where the learner sequentially receives a side information vector and has to choose an action in a convex set, minimizing a funct…
Detection boundary in sparse regression
Yuri I. Ingster, Alexandre B. Tsybakov, Nicolas Verzelen
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the…