Related papers: Data-driven Competitive Algorithms for Online Knap…
We study the incremental knapsack problem, where one wishes to sequentially pack items into a knapsack whose capacity expands over a finite planning horizon, with the objective of maximizing time-averaged profits. While various…
We study learning optimal policies from a logged dataset, i.e., offline RL, with function approximation. Despite the efforts devoted, existing algorithms with theoretic finite-sample guarantees typically assume exploratory data coverage or…
We approach the fundamental problem of obstacle avoidance for robotic systems via the lens of online learning. In contrast to prior work that either assumes worst-case realizations of uncertainty in the environment or a stationary…
The challenge in the widely applicable online matching problem lies in making irrevocable assignments while there is uncertainty about future inputs. Most theoretically-grounded policies are myopic or greedy in nature. In real-world…
We study the framework of a dynamic decision-making scenario with resource constraints. In this framework, an agent, whose target is to maximize the total reward under the initial inventory, selects an action in each round upon observing a…
We consider the online $k$-median clustering problem in which $n$ points arrive online and must be irrevocably assigned to a cluster on arrival. As there are lower bound instances that show that an online algorithm cannot achieve a…
Rollout algorithms have demonstrated excellent performance on a variety of dynamic and discrete optimization problems. Interpreted as an approximate dynamic programming algorithm, a rollout algorithm estimates the value-to-go at each…
In the random-order online set cover problem, the instance with $m$ sets and $n$ elements is chosen in a worst-case fashion, but then the elements arrive in a uniformly random order. Can this random-order model allow us to circumvent the…
Display Ads and the generalized assignment problem are two well-studied online packing problems with important applications in ad allocation and other areas. In both problems, ad impressions arrive online and have to be allocated…
Effective caching is crucial for the performance of modern-day computing systems. A key optimization problem arising in caching -- which item to evict to make room for a new item -- cannot be optimally solved without knowing the future.…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
We consider the online vector packing problem in which we have a $d$ dimensional knapsack and items $u$ with weight vectors $\mathbf{w}_u \in \mathbb{R}_+^d$ arrive online in an arbitrary order. Upon the arrival of an item, the algorithm…
Achieving both optimality and safety under unknown system dynamics is a central challenge in real-world deployment of agents. To address this, we introduce a notion of maximum safe dynamics learning, where sufficient exploration is…
We consider the problem of learning and using predictions for warm start algorithms with predictions. In this setting, an algorithm is given an instance of a problem, and a prediction of the solution. The runtime of the algorithm is bounded…
Obtaining strong linear relaxations of capacitated covering problems constitute a major technical challenge even for simple settings. For one of the most basic cases, the Knapsack-Cover (Min-Knapsack) problem, the relaxation based on…
A frequently studied performance measure in online optimization is competitive analysis. It corresponds to the worst-case ratio, over all possible inputs of an algorithm, between the performance of the algorithm and the optimal offline…
We consider the fundamental problem of online control of a linear dynamical system from two different viewpoints: regret minimization and competitive analysis. We prove that the optimal competitive policy is well-approximated by a convex…
In this paper, we study the peak-aware energy scheduling problem using the competitive framework with machine learning prediction. With the uncertainty of energy demand as the fundamental challenge, the goal is to schedule the energy output…
We consider the online bin packing problem under the advice complexity model where the 'online constraint' is relaxed and an algorithm receives partial information about the future requests. We provide tight upper and lower bounds for the…