The Quadratic Unconstrained Binary Optimization (QUBO) modeling and solution framework is required for quantum and digital annealers whose goal is the optimization of a well defined metric, the objective function. However, diverse suboptimal solutions may be preferred over harder to implement strict optimal ones. In addition, the decision-maker usually has insights that are not always efficiently translated into the optimization model, such as acceptable target, interval or range values. Multi-criteria decision making is an example of involving the user in the decision process. In this paper, we present two variants of goal-seeking QUBO that minimize the deviation from the goal through a tabu-search based greedy one-flip heuristic. Experimental results illustrate the efficacy of the proposed approach over Constraint Programming for quickly finding a satisficing set of solutions.

Many applications in machine learning can be framed as minimization problems and solved efficiently using gradient-based techniques. However, recent applications of generative models, particularly GANs, have triggered interest in solving min-max games for which standard optimization techniques are often not suitable. Among known problems experienced by practitioners is the lack of convergence guarantees or convergence to a non-optimum cycle. At the heart of these problems is the min-max structure of the GAN objective which creates non-trivial dependencies between the players. We propose to address this problem by optimizing a different objective that circumvents the min-max structure using the notion of duality gap from game theory. We provide novel convergence guarantees on this objective and demonstrate why the obtained limit point solves the problem better than known techniques.

Multi-robot task allocation is one of the most fundamental classes of problems in robotics and is crucial for various real-world robotic applications such as search, rescue and area exploration. We consider the Single-Task robots and Multi-Robot tasks Instantaneous Assignment (ST-MR-IA) setting where each task requires at least a certain number of robots and each robot can work on at most one task and incurs an operational cost for each task. Our aim is to consider a natural computational problem of allocating robots to complete the maximum number of tasks subject to budget constraints. We consider budget constraints of three different kinds: (1) total budget, (2) task budget, and (3) robot budget. We provide a detailed complexity analysis including results on approximations as well as polynomial-time algorithms for the general setting and important restricted settings.

Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, $L_2$ regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some systems, such as satellites, the control needs to be applied in sparse bursts due to how the propulsion system operates. In this paper, we study approaches to induce sparsity in optimal control solutions -- namely via smooth $L_1$ and Huber regularization penalties. We apply these loss terms to state-of-the-art DDP-based solvers to create a family of sparsity-inducing optimal control methods. We analyze and compare the effect of the different losses on inducing sparsity, their numerical conditioning, their impact on convergence, and discuss hyperparameter settings. We demonstrate our method in simulation and hardware experiments on canonical dynamics systems, control of satellites, and the NASA Valkyrie humanoid robot. We provide an implementation of our method and all examples for reproducibility on GitHub.

The contribution of this paper includes two aspects. First, we study the lower bound complexity for the minimax optimization problem whose objective function is the average of $n$ individual smooth component functions. We consider Proximal Incremental First-order (PIFO) algorithms which have access to gradient and proximal oracle for each individual component. We develop a novel approach for constructing adversarial problems, which partitions the tridiagonal matrix of classical examples into $n$ groups. This construction is friendly to the analysis of incremental gradient and proximal oracle. With this approach, we demonstrate the lower bounds of first-order algorithms for finding an $\varepsilon$-suboptimal point and an $\varepsilon$-stationary point in different settings. Second, we also derive the lower bounds of minimization optimization with PIFO algorithms from our approach, which can cover the results in \citep{woodworth2016tight} and improve the results in \citep{zhou2019lower}.

Machine learning (ML) is successful in achieving human-level performance in various fields. However, it lacks the ability to explain an outcome due to its black-box nature. While existing explainable ML is promising, almost all of these methods focus on formatting interpretability as an optimization problem. Such a mapping leads to numerous iterations of time-consuming complex computations, which limits their applicability in real-time applications. In this paper, we propose a novel framework for accelerating explainable ML using Tensor Processing Units (TPUs). The proposed framework exploits the synergy between matrix convolution and Fourier transform, and takes full advantage of TPU's natural ability in accelerating matrix computations. Specifically, this paper makes three important contributions. (1) To the best of our knowledge, our proposed work is the first attempt in enabling hardware acceleration of explainable ML using TPUs. (2) Our proposed approach is applicable across a wide variety of ML algorithms, and effective utilization of TPU-based acceleration can lead to real-time outcome interpretation. (3) Extensive experimental results demonstrate that our proposed approach can provide an order-of-magnitude speedup in both classification time (25x on average) and interpretation time (13x on average) compared to state-of-the-art techniques.

Policy optimization methods remain a powerful workhorse in empirical Reinforcement Learning (RL), with a focus on neural policies that can easily reason over complex and continuous state and/or action spaces. Theoretical understanding of strategic exploration in policy-based methods with non-linear function approximation, however, is largely missing. In this paper, we address this question by designing ENIAC, an actor-critic method that allows non-linear function approximation in the critic. We show that under certain assumptions, e.g., a bounded eluder dimension $d$ for the critic class, the learner finds a near-optimal policy in $O(\poly(d))$ exploration rounds. The method is robust to model misspecification and strictly extends existing works on linear function approximation. We also develop some computational optimizations of our approach with slightly worse statistical guarantees and an empirical adaptation building on existing deep RL tools. We empirically evaluate this adaptation and show that it outperforms prior heuristics inspired by linear methods, establishing the value via correctly reasoning about the agent's uncertainty under non-linear function approximation.

This paper presents and discusses algorithms, hardware, and software architecture developed by the TEAM CoSTAR (Collaborative SubTerranean Autonomous Robots), competing in the DARPA Subterranean Challenge. Specifically, it presents the techniques utilized within the Tunnel (2019) and Urban (2020) competitions, where CoSTAR achieved 2nd and 1st place, respectively. We also discuss CoSTAR's demonstrations in Martian-analog surface and subsurface (lava tubes) exploration. The paper introduces our autonomy solution, referred to as NeBula (Networked Belief-aware Perceptual Autonomy). NeBula is an uncertainty-aware framework that aims at enabling resilient and modular autonomy solutions by performing reasoning and decision making in the belief space (space of probability distributions over the robot and world states). We discuss various components of the NeBula framework, including: (i) geometric and semantic environment mapping; (ii) a multi-modal positioning system; (iii) traversability analysis and local planning; (iv) global motion planning and exploration behavior; (i) risk-aware mission planning; (vi) networking and decentralized reasoning; and (vii) learning-enabled adaptation. We discuss the performance of NeBula on several robot types (e.g. wheeled, legged, flying), in various environments. We discuss the specific results and lessons learned from fielding this solution in the challenging courses of the DARPA Subterranean Challenge competition.

With mathematical optimization, companies can capture the key features of their business problems in an optimization model and can generate optimal solutions (which are used as the basis to make optimal decisions). Data scientists with some basic mathematical programming skills can easily learn how to build, implement, and maintain mathematical optimization applications. The Gurobi Python API borrows ideas from modeling languages, enabling users to deploy and solve mathematical optimization models with scripts that are easy to write, read, and maintain. Such modules can even be embedded in decision support systems for production-ready applications.

Lawrence Livermore National Laboratory (LLNL) computer scientists have developed a new framework and an accompanying visualization tool that leverages deep reinforcement learning for symbolic regression problems, outperforming baseline methods on benchmark problems. The paper was recently accepted as an oral presentation at the International Conference on Learning Representations (ICLR 2021), one of the top machine learning conferences in the world. The conference takes place virtually May 3-7. In the paper, the LLNL team describes applying deep reinforcement learning to discrete optimization--problems that deal with discrete "building blocks" that must be combined in a particular order or configuration to optimize a desired property. The team focused on a type of discrete optimization called symbolic regression--finding short mathematical expressions that fit data gathered from an experiment.