Related papers: Convex Methods for Constrained Linear Bandits
We consider a safe optimization problem with bandit feedback in which an agent sequentially chooses actions and observes responses from the environment, with the goal of maximizing an arbitrary function of the response while respecting…
Efficient methods to provide sub-optimal solutions to non-convex optimization problems with knowledge of the solution's sub-optimality would facilitate the widespread application of nonlinear optimal control algorithms. To that end,…
We develop a framework for convexifying a fairly general class of optimization problems. Under additional assumptions, we analyze the suboptimality of the solution to the convexified problem relative to the original nonconvex problem and…
Unlike classical control theory, such as Linear Quadratic Control (LQC), real-world control problems are highly complex. These problems often involve adversarial perturbations, bandit feedback models, and non-quadratic, adversarially chosen…
This paper studies bandit convex optimization in non-stationary environments with two-point feedback, using dynamic regret as the performance measure. We propose an algorithm based on bandit mirror descent that extends naturally to…
The RKHS bandit problem (also called kernelized multi-armed bandit problem) is an online optimization problem of non-linear functions with noisy feedback. Although the problem has been extensively studied, there are unsatisfactory results…
We consider the decision-making framework of online convex optimization with a very large number of experts. This setting is ubiquitous in contextual and reinforcement learning problems, where the size of the policy class renders…
Linear bandit algorithms yield $\tilde{\mathcal{O}}(n\sqrt{T})$ pseudo-regret bounds on compact convex action sets $\mathcal{K}\subset\mathbb{R}^n$ and two types of structural assumptions lead to better pseudo-regret bounds. When…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
High-quality data plays a central role in ensuring the accuracy of policy evaluation. This paper initiates the study of efficient and safe data collection for bandit policy evaluation. We formulate the problem and investigate its several…
This brief paper presents simple simulation-based algorithms for obtaining an approximately optimal policy in a given finite set in large finite constrained Markov decision processes. The algorithms are adapted from playing strategies for…
Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…
We investigate an active pure-exploration setting, that includes best-arm identification, in the context of linear stochastic bandits. While asymptotically optimal algorithms exist for standard multi-arm bandits, the existence of such…
We consider bandit problems involving a large (possibly infinite) collection of arms, in which the expected reward of each arm is a linear function of an $r$-dimensional random vector $\mathbf{Z} \in \mathbb{R}^r$, where $r \geq 2$. The…
In today's business marketplace, many high-tech Internet enterprises constantly explore innovative ways to provide optimal online user experiences for gaining competitive advantages. The great needs of developing intelligent interactive…
Solving linear programs is often a challenging task in distributed settings. While there are good algorithms for solving packing and covering linear programs in a distributed manner (Kuhn et al.~2006), this is essentially the only class of…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
This study presents two new algorithms for solving linear stochastic bandit problems. The proposed methods use an approach from non-parametric statistics called bootstrapping to create confidence bounds. This is achieved without making any…
Lagrangian relaxation and approximate optimization algorithms have received much attention in the last two decades. Typically, the running time of these methods to obtain a $\epsilon$ approximate solution is proportional to…
Bandit algorithms have garnered significant attention due to their practical applications in real-world scenarios. However, beyond simple settings such as multi-arm or linear bandits, optimal algorithms remain scarce. Notably, no optimal…