Junyan Liu

Longfei Wang, Junyan Liu, Fan Zhang et al.

Parallelization has emerged as a promising approach for accelerating MILP solving. However, the complexity of the branch-and-bound (B&B) framework and the numerous effective algorithm components in MILP solvers make it difficult to parallelize. In this study, a scalable parallel framework, N2N (a node-to-node framework that maps the B&B nodes to distributed computing nodes), was proposed to solve large-scale problems in a distributed memory computing environment. Both deterministic and nondeterministic modes are supported, and the framework is designed to be easily integrated with existing solvers. Regarding the deterministic mode, a novel sliding-window-based algorithm was designed and implemented to ensure that tasks are generated and solved in a deterministic order. Moreover, several advanced techniques, such as the utilization of CP search and general primal heuristics, have been developed to fully utilize distributed computing resources and capabilities of base solvers. Adaptive solving and data communication optimization were also investigated. A popular open-source MILP solver, SCIP, was integrated into N2N as the base solver, yielding N2N-SCIP. Extensive computational experiments were conducted to evaluate the performance of N2N-SCIP compared to ParaSCIP, which is a state-of-the-art distributed parallel MILP solver under the UG framework. The nondeterministic N2N-SCIP achieves speedups of 22.52 and 12.71 with 1,000 MPI processes on the Kunpeng and x86 computing clusters, which is 1.98 and 2.08 times faster than ParaSCIP, respectively. In the deterministic mode, N2N-SCIP also shows significant performance improvements over ParaSCIP across different process numbers and computing clusters. To validate the generality of N2N, HiGHS, another open-source solver, was integrated into N2N. The related results are analyzed, and the requirements of N2N on base solvers are also concluded.

Junyan Liu, Lillian J. Ratliff

We study the repeated principal-agent bandit game, where the principal indirectly interacts with the unknown environment by proposing incentives for the agent to play arms. Most existing work assumes the agent has full knowledge of the reward means and always behaves greedily, but in many online marketplaces, the agent needs to learn the unknown environment and sometimes explore. Motivated by such settings, we model a self-interested learning agent with exploration behaviors who iteratively updates reward estimates and either selects an arm that maximizes the estimated reward plus incentive or explores arbitrarily with a certain probability. As a warm-up, we first consider a self-interested learning agent without exploration. We propose algorithms for both i.i.d. and linear reward settings with bandit feedback in a finite horizon $T$, achieving regret bounds of $\widetilde{O}(\sqrt{T})$ and $\widetilde{O}( T^{2/3} )$, respectively. Specifically, these algorithms are established upon a novel elimination framework coupled with newly-developed search algorithms which accommodate the uncertainty arising from the learning behavior of the agent. We then extend the framework to handle the exploratory learning agent and develop an algorithm to achieve a $\widetilde{O}(T^{2/3})$ regret bound in i.i.d. reward setup by enhancing the robustness of our elimination framework to the potential agent exploration. Finally, when reducing our agent behaviors to the one studied in (Dogan et al., 2023a), we propose an algorithm based on our robust framework, which achieves a $\widetilde{O}(\sqrt{T})$ regret bound, significantly improving upon their $\widetilde{O}(T^{11/12})$ bound.

Junyan Liu, Arnab Maiti, Artin Tajdini et al.

We initiate the study of a repeated principal-agent problem over a finite horizon $T$, where a principal sequentially interacts with $K\geq 2$ types of agents arriving in an adversarial order. At each round, the principal strategically chooses one of the $N$ arms to incentivize for an arriving agent of unknown type. The agent then chooses an arm based on its own utility and the provided incentive, and the principal receives a corresponding reward. The objective is to minimize regret against the best incentive in hindsight. Without prior knowledge of agent behavior, we show that the problem becomes intractable, leading to linear regret. We analyze two key settings where sublinear regret is achievable. In the first setting, the principal knows the arm each agent type would select greedily for any given incentive. Under this setting, we propose an algorithm that achieves a regret bound of $O(\min\{\sqrt{KT\log N},K\sqrt{T}\})$ and provide a matching lower bound up to a $\log K$ factor. In the second setting, an agent's response varies smoothly with the incentive and is governed by a Lipschitz constant $L\geq 1$. Under this setting, we show that there is an algorithm with a regret bound of $\tilde{O}((LN)^{1/3}T^{2/3})$ and establish a matching lower bound up to logarithmic factors. Finally, we extend our algorithmic results for both settings by allowing the principal to incentivize multiple arms simultaneously in each round.

Junyan Liu, Ziyun Chen, Kun Wang et al.

We study the Pandora's Box problem in an online learning setting with semi-bandit feedback. In each round, the learner sequentially pays to open up to $n$ boxes with unknown reward distributions, observes rewards upon opening, and decides when to stop. The utility of the learner is the maximum observed reward minus the cumulative cost of opened boxes, and the goal is to minimize regret defined as the gap between the cumulative expected utility and that of the optimal policy. We propose a new algorithm that achieves $\widetilde{O}(\sqrt{nT})$ regret after $T$ rounds, which improves the $\widetilde{O}(n\sqrt{T})$ bound of Agarwal et al. [2024] and matches the known lower bound up to logarithmic factors. To better capture real-life applications, we then extend our results to a natural but challenging contextual linear setting, where each box's expected reward is linear in some known but time-varying $d$-dimensional context and the noise distribution is fixed over time. We design an algorithm that learns both the linear function and the noise distributions, achieving $\widetilde{O}(nd\sqrt{T})$ regret. Finally, we show that our techniques also apply to the online Prophet Inequality problem, where the learner must decide immediately whether or not to accept a revealed reward. In both non-contextual and contextual settings, our approach achieves similar improvements and regret bounds.

Tiancheng Jin, Junyan Liu, Chloé Rouyer et al.

Existing online learning algorithms for adversarial Markov Decision Processes achieve ${O}(\sqrt{T})$ regret after $T$ rounds of interactions even if the loss functions are chosen arbitrarily by an adversary, with the caveat that the transition function has to be fixed. This is because it has been shown that adversarial transition functions make no-regret learning impossible. Despite such impossibility results, in this work, we develop algorithms that can handle both adversarial losses and adversarial transitions, with regret increasing smoothly in the degree of maliciousness of the adversary. More concretely, we first propose an algorithm that enjoys $\widetilde{O}(\sqrt{T} + C^{\textsf{P}})$ regret where $C^{\textsf{P}}$ measures how adversarial the transition functions are and can be at most ${O}(T)$. While this algorithm itself requires knowledge of $C^{\textsf{P}}$, we further develop a black-box reduction approach that removes this requirement. Moreover, we also show that further refinements of the algorithm not only maintains the same regret bound, but also simultaneously adapts to easier environments (where losses are generated in a certain stochastically constrained manner as in Jin et al. [2021]) and achieves $\widetilde{O}(U + \sqrt{UC^{\textsf{L}}} + C^{\textsf{P}})$ regret, where $U$ is some standard gap-dependent coefficient and $C^{\textsf{L}}$ is the amount of corruption on losses.