The results are based on anovelanalysis ofreal-time dynamic programming, thenextended tomodel-based RL.Specifically,wegeneralize existing algorithms that perform full-planning to act by 1-step planning.

We study the constrained reinforcement learning problem, in which an agent aims tomaximize the expected cumulativereward subject toaconstraint on the expected total value of a utility function. In contrast to existing model-based approaches or model-free methods accompanied with a'simulator', we aim to develop thefirst model-free, simulator-freealgorithm that achieves a sublinear regret and a sublinear constraint violation even inlarge-scale systems.

State-of-the-art efficient model-based Reinforcement Learning (RL) algorithms typically act by iteratively solving empirical models, i.e., by performing full-planning on Markov Decision Processes (MDPs) built by the gathered experience. In this paper, we focus on model-based RL in the finite-state finite-horizon MDP setting and establish that exploring with greedy policies -- act by 1-step planning -- can achieve tight minimax performance in terms of regret, O(\sqrt{HSAT}). Thus, full-planning in model-based RL can be avoided altogether without any performance degradation, and, by doing so, the computational complexity decreases by a factor of S. The results are based on a novel analysis of real-time dynamic programming, then extended to model-based RL. Specifically, we generalize existing algorithms that perform full-planning to such that act by 1-step planning. For these generalizations, we prove regret bounds with the same rate as their full-planning counterparts.

In this work, we consider learning-based applications in routing to solve a Vehicle Routing variant characterized by stochasticity and multiple objectives. Such problems are representative of practical settings where decision-makers have to deal with uncertainty in the operational environment as well as multiple conflicting objectives due to different stakeholders. We specifically consider travel time uncertainty. We also consider two objectives, total travel time and route makespan, that jointly target operational efficiency and labor regulations on shift length, although different objectives could be incorporated. Learning-based methods offer earnest computational advantages as they can repeatedly solve problems with limited interference from the decision-maker. We specifically focus on end-to-end deep learning models that leverage the attention mechanism and multiple solution trajectories. These models have seen several successful applications in routing problems. However, since travel times are not a direct input to these models due to the large dimensions of the travel time matrix, accounting for uncertainty is a challenge, especially in the presence of multiple objectives. In turn, we propose a model that simultaneously addresses stochasticity and multi-objectivity and provide a refined training mechanism for this model through scenario clustering to reduce training time. Our results show that our model is capable of constructing a Pareto Front of good quality within acceptable run times compared to three baselines.

In this framework, the objective is to find a policy for making decisions that maximizes the value of some utility function.

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We introduce the community exploration problem that has many real-world applications such as online advertising.

We argue that this assumption is rarely verified in practice, as the recommendation process itself may impact the user's