Consider a learning algorithm, which involves an internal call to an optimization routine such as a generalized eigenvalue problem, a cone programming problem or even sorting. Integrating such a method as a layer(s) within a trainable deep neural network (DNN) in an efficient and numerically stable way is not straightforward -- for instance, only recently, strategies have emerged for eigendecomposition and differentiable sorting. We propose an efficient and differentiable solver for general linear programming problems which can be used in a plug and play manner within DNNs as a layer. Our development is inspired by a fascinating but not widely used link between dynamics of slime mold (physarum) and optimization schemes such as steepest descent. We describe our development and show the use of our solver in a video segmentation task and meta-learning for few-shot learning. We review the existing results and provide a technical analysis describing its applicability for our use cases. Our solver performs comparably with a customized projected gradient descent method on the first task and outperforms the differentiable CVXPY-SCS solver on the second task. Experiments show that our solver converges quickly without the need for a feasible initial point. Our proposal is easy to implement and can easily serve as layers whenever a learning procedure needs a fast approximate solution to a LP, within a larger network.

Multi-objective controller synthesis concerns the problem of computing an optimal controller subject to multiple (possibly conflicting) objective properties. The relative importance of objectives is often specified by human decision-makers. However, there is inherent uncertainty in human preferences (e.g., due to different preference elicitation methods). In this paper, we formalize the notion of uncertain human preferences and present a novel approach that accounts for uncertain human preferences in the multi-objective controller synthesis for Markov decision processes (MDPs). Our approach is based on mixed-integer linear programming (MILP) and synthesizes a sound, optimally permissive multi-strategy with respect to a multi-objective property and an uncertain set of human preferences. Experimental results on a range of large case studies show that our MILP-based approach is feasible and scalable to synthesize sound, optimally permissive multi-strategies with varying MDP model sizes and uncertainty levels of human preferences. Evaluation via an online user study also demonstrates the quality and benefits of synthesized (multi-)strategies.

Markov Decision Processes (MDPs) play key mathematical models in Reinforcement Learning (RL). Despite its success in empirical performances [Haarnoja et al., 2018, Mnih et al., 2015, 2016, Silver et al., 2016], there are also many works providing insightful and solid theoretical understandings towards RL. The difficulty of solving an MDP mainly is due to the reward and transition probability, whose exact information is usually unknown to observers. To deal with the situations, one common approach resorts to offline methods, where the agent only has access to a given explorable dataset generated by given strategies. Many practical deep RL algorithms employ the offline method and achieve state-of-art success [Mnih et al., 2015, Lillicrap et al., 2015, Fujimoto et al., 2019]. In addition to empirical success, there are flourishing works on offline RL from a theoretical perspective. Some prior works [Chen and Jiang, 2019, Agarwal et al., 2020, Duan et al., 2021] have provided solid results on model-free offline methods, while some other works [Sidford et al., 2018, Xie et al., 2019, Yin and Wang, 2020, Yin et al., 2020] consider model-based approaches. However, Mannor et al. [2004] showed that model-based approaches can be quite sensitive to estimation errors by directly estimating the transition probability from an offline dataset.

As a projection-free algorithm, Frank-Wolfe (FW) method, also known as conditional gradient, has recently received considerable attention in the machine learning community. In this dissertation, we study several topics on the FW variants for scalable projection-free optimization. We first propose 1-SFW, the first projection-free method that requires only one sample per iteration to update the optimization variable and yet achieves the best known complexity bounds for convex, non-convex, and monotone DR-submodular settings. Then we move forward to the distributed setting, and develop Quantized Frank-Wolfe (QFW), a general communication-efficient distributed FW framework for both convex and non-convex objective functions. We study the performance of QFW in two widely recognized settings: 1) stochastic optimization and 2) finite-sum optimization. Finally, we propose Black-Box Continuous Greedy, a derivative-free and projection-free algorithm, that maximizes a monotone continuous DR-submodular function over a bounded convex body in Euclidean space.

We consider the problem of extracting joint and individual signals from multi-view data, that is data collected from different sources on matched samples. While existing methods for multi-view data decomposition explore single matching of data by samples, we focus on double-matched multi-view data (matched by both samples and source features). Our motivating example is the miRNA data collected from both primary tumor and normal tissues of the same subjects; the measurements from two tissues are thus matched both by subjects and by miRNAs. Our proposed double-matched matrix decomposition allows to simultaneously extract joint and individual signals across subjects, as well as joint and individual signals across miRNAs. Our estimation approach takes advantage of double-matching by formulating a new type of optimization problem with explicit row space and column space constraints, for which we develop an efficient iterative algorithm. Numerical studies indicate that taking advantage of double-matching leads to superior signal estimation performance compared to existing multi-view data decomposition based on single-matching. We apply our method to miRNA data as well as data from the English Premier League soccer matches, and find joint and individual multi-view signals that align with domain specific knowledge.

The manpower scheduling problem is a critical research field in the resource management area. Based on the existing studies on scheduling problem solutions, this paper transforms the manpower scheduling problem into a combinational optimization problem under multi-constraint conditions from a new perspective. It also uses logical paradigms to build a mathematical model for problem solution and an improved multi-dimensional evolution algorithm for solving the model. Moreover, the constraints discussed in this paper basically cover all the requirements of human resource coordination in modern society and are supported by our experiment results. In the discussion part, we compare our model with other heuristic algorithms or linear programming methods and prove that the model proposed in this paper makes a 25.7% increase in efficiency and a 17% increase in accuracy at most. In addition, to the numerical solution of the manpower scheduling problem, this paper also studies the algorithm for scheduling task list generation and the method of displaying scheduling results. As a result, we not only provide various modifications for the basic algorithm to solve different condition problems but also propose a new algorithm that increases at least 28.91% in time efficiency by comparing with different baseline models.

Constrained optimization solvers with Integer Linear programming (ILP) have been the cornerstone for explainable natural language inference during its inception. ILP based approaches provide a way to encode explicit and controllable assumptions casting natural language inference as an abductive reasoning problem, where the solver constructs a plausible explanation for a given hypothesis. While constrained based solvers provide explanations, they are often limited by the use of explicit constraints and cannot be integrated as part of broader deep neural architectures. In contrast, state-of-the-art transformer-based models can learn from data and implicitly encode complex constraints. However, these models are intrinsically black boxes. This paper presents a novel framework named $\partial$-Explainer (Diff-Explainer) that combines the best of both worlds by casting the constrained optimization as part of a deep neural network via differentiable convex optimization and fine-tuning pre-trained transformers for downstream explainable NLP tasks. To demonstrate the efficacy of the framework, we transform the constraints presented by TupleILP and integrate them with sentence embedding transformers for the task of explainable science QA. Our experiments show up to $\approx 10\%$ improvement over non-differentiable solver while still providing explanations for supporting its inference.

It has recently been shown that reinforcement learning can be used to train generators capable of producing high-quality game levels, with quality defined in terms of some user-specified heuristic. To ensure that these generators' output is sufficiently diverse (that is, not amounting to the reproduction of a single optimal level configuration), the generation process is constrained such that the initial seed results in some variance in the generator's output. However, this results in a loss of control over the generated content for the human user. We propose to train generators capable of producing controllably diverse output, by making them "goal-aware." To this end, we add conditional inputs representing how close a generator is to some heuristic, and also modify the reward mechanism to incorporate that value. Testing on multiple domains, we show that the resulting level generators are capable of exploring the space of possible levels in a targeted, controllable manner, producing levels of comparable quality as their goal-unaware counterparts, that are diverse along designer-specified dimensions.

Deep reinforcement learning (DRL) has recently shown its success in tackling complex combinatorial optimization problems. When these problems are extended to multiobjective ones, it becomes difficult for the existing DRL approaches to flexibly and efficiently deal with multiple subproblems determined by weight decomposition of objectives. This paper proposes a concise meta-learning-based DRL approach. It first trains a meta-model by meta-learning. The meta-model is fine-tuned with a few update steps to derive submodels for the corresponding subproblems. The Pareto front is built accordingly. The computational experiments on multiobjective traveling salesman problems demonstrate the superiority of our method over most of learning-based and iteration-based approaches.

Traffic congestion has large economic and social costs. The introduction of autonomous vehicles can potentially reduce this congestion by increasing road capacity via vehicle platooning and by creating an avenue for influencing people's choice of routes. We consider a network of parallel roads with two modes of transportation: (i) human drivers, who will choose the quickest route available to them, and (ii) a ride hailing service, which provides an array of autonomous vehicle route options, each with different prices, to users. We formalize a model of vehicle flow in mixed autonomy and a model of how autonomous service users make choices between routes with different prices and latencies. Developing an algorithm to learn the preferences of the users, we formulate a planning optimization that chooses prices to maximize a social objective. We demonstrate the benefit of the proposed scheme by comparing the results to theoretical benchmarks which we show can be efficiently calculated.