Motivated by the increasing adoption of models which facilitate greater automation in risk management and decision-making, this paper presents a novel Importance Sampling (IS) scheme for measuring distribution tails of objectives modelled with enabling tools such as feature-based decision rules, mixed integer linear programs, deep neural networks, etc. Conventional efficient IS approaches suffer from feasibility and scalability concerns due to the need to intricately tailor the sampler to the underlying probability distribution and the objective. This challenge is overcome in the proposed black-box scheme by automating the selection of an effective IS distribution with a transformation that implicitly learns and replicates the concentration properties observed in less rare samples. This novel approach is guided by a large deviations principle that brings out the phenomenon of self-similarity of optimal IS distributions. The proposed sampler is the first to attain asymptotically optimal variance reduction across a spectrum of multivariate distributions despite being oblivious to the underlying structure. The large deviations principle additionally results in new distribution tail asymptotics capable of yielding operational insights. The applicability is illustrated by considering product distribution networks and portfolio credit risk models informed by neural networks as examples.

We consider a decision maker who must choose an action in order to maximize a reward function that depends also on an unknown parameter {\Theta}. The decision maker can delay taking the action in order to experiment and gather additional information on {\Theta}. We model the decision maker's problem using a Bayesian sequential experimentation framework and use dynamic programming and diffusion-asymptotic analysis to solve it. For that, we scale our problem in a way that both the average number of experiments that is conducted per unit of time is large and the informativeness of each individual experiment is low. Under such regime, we derive a diffusion approximation for the sequential experimentation problem, which provides a number of important insights about the nature of the problem and its solution. Our solution method also shows that the complexity of the problem grows only quadratically with the cardinality of the set of actions from which the decision maker can choose. We illustrate our methodology and results using a concrete application in the context of assortment selection and new product introduction. Specifically, we study the problem of a seller who wants to select an optimal assortment of products to launch into the marketplace and is uncertain about consumers' preferences. Motivated by emerging practices in e-commerce, we assume that the seller is able to use a crowdvoting system to learn these preferences before a final assortment decision is made. In this context, we undertake an extensive numerical analysis to assess the value of learning and demonstrate the effectiveness and robustness of the heuristics derived from the diffusion approximation.

This paper outlines the ideas behind developing a graph-based heuristic-driven routing algorithm designed for a particular instance of a goods transportation problem with a single good type. The proposed algorithm solves the optimization problem of satisfying the demand of goods on a given undirected transportation graph with minimizing the estimated cost for each traversed segment of the delivery path. The operation of the routing algorithm is discussed and overall evaluation of the proposed problem solving technique is given. HE transportation problem is one of the well-known and hot topics both in mathematics and economics. It was first conceptualized by the French mathematician Gaspard Monge back in 1781 [1].

Projection-free conditional gradient (CG) methods are the algorithms of choice for constrained optimization setups in which projections are often computationally prohibitive but linear optimization over the constraint set remains computationally feasible. Unlike in projection-based methods, globally accelerated convergence rates are in general unattainable for CG. However, a very recent work on Locally accelerated CG (LaCG) has demonstrated that local acceleration for CG is possible for many settings of interest. The main downside of LaCG is that it requires knowledge of the smoothness and strong convexity parameters of the objective function. We remove this limitation by introducing a novel, Parameter-Free Locally accelerated CG (PF-LaCG) algorithm, for which we provide rigorous convergence guarantees. Our theoretical results are complemented by numerical experiments, which demonstrate local acceleration and showcase the practical improvements of PF-LaCG over non-accelerated algorithms, both in terms of iteration count and wall-clock time.

Scalable Gaussian Process methods are computationally attractive, yet introduce modeling biases that require rigorous study. This paper analyzes two common techniques: early truncated conjugate gradients (CG) and random Fourier features (RFF). We find that both methods introduce a systematic bias on the learned hyperparameters: CG tends to underfit while RFF tends to overfit. We address these issues using randomized truncation estimators that eliminate bias in exchange for increased variance. In the case of RFF, we show that the bias-to-variance conversion is indeed a trade-off: the additional variance proves detrimental to optimization. However, in the case of CG, our unbiased learning procedure meaningfully outperforms its biased counterpart with minimal additional computation.

Several large-scale machine learning tasks, such as data summarization, can be approached by maximizing functions that satisfy submodularity. These optimization problems often involve complex side constraints, imposed by the underlying application. In this paper, we develop an algorithm with poly-logarithmic adaptivity for non-monotone submodular maximization under general side constraints. The adaptive complexity of a problem is the minimal number of sequential rounds required to achieve the objective. Our algorithm is suitable to maximize a non-monotone submodular function under a $p$-system side constraint, and it achieves a $(p + O(\sqrt{p}))$-approximation for this problem, after only poly-logarithmic adaptive rounds and polynomial queries to the valuation oracle function. Furthermore, our algorithm achieves a $(p + O(1))$-approximation when the given side constraint is a $p$-extendible system. This algorithm yields an exponential speed-up, with respect to the adaptivity, over any other known constant-factor approximation algorithm for this problem. It also competes with previous known results in terms of the query complexity. We perform various experiments on various real-world applications. We find that, in comparison with commonly used heuristics, our algorithm performs better on these instances.

Many reinforcement learning algorithms can be seen as versions of approximate policy iteration (API). While standard API often performs poorly, it has been shown that learning can be stabilized by regularizing each policy update by the KL-divergence to the previous policy. Popular practical algorithms such as TRPO, MPO, and VMPO replace regularization by a constraint on KL-divergence of consecutive policies, arguing that this is easier to implement and tune. In this work, we study this implementation choice in more detail. We compare the use of KL divergence as a constraint vs. as a regularizer, and point out several optimization issues with the widely-used constrained approach. We show that the constrained algorithm is not guaranteed to converge even on simple problem instances where the constrained problem can be solved exactly, and in fact incurs linear expected regret. With approximate implementation using softmax policies, we show that regularization can improve the optimization landscape of the original objective. We demonstrate these issues empirically on several bandit and RL environments.

The published literature on topology optimization has exploded over the last two decades to include methods that use shape and topological derivatives or evolutionary algorithms formulated on various geometric representations and parametrizations. One of the key challenges of all these methods is the massive computational cost associated with 3D topology optimization problems. We introduce a transfer learning method based on a convolutional neural network that (1) can handle high-resolution 3D design domains of various shapes and topologies; (2) supports real-time design space explorations as the domain and boundary conditions change; (3) requires a much smaller set of high-resolution examples for the improvement of learning in a new task compared to traditional deep learning networks; (4) is multiple orders of magnitude more efficient than the established gradient-based methods, such as SIMP. We provide numerous 2D and 3D examples to showcase the effectiveness and accuracy of our proposed approach, including for design domains that are unseen to our source network, as well as the generalization capabilities of the transfer learning-based approach. Our experiments achieved an average binary accuracy of around 95% at real-time prediction rates. These properties, in turn, suggest that the proposed transfer-learning method may serve as the first practical underlying framework for real-time 3D design exploration based on topology optimization

Data driven models of dynamical systems help planners and controllers to provide more precise and accurate motions. Most model learning algorithms will try to minimize a loss function between the observed data and the model's predictions. This can be improved using prior knowledge about the task at hand, which can be encoded in the form of constraints. This turns the unconstrained model learning problem into a constrained one. These constraints allow models with finite capacity to focus their expressive power on important aspects of the system. This can lead to models that are better suited for certain tasks. This paper introduces the constrained Sufficiently Accurate model learning approach, provides examples of such problems, and presents a theorem on how close some approximate solutions can be. The approximate solution quality will depend on the function parameterization, loss and constraint function smoothness, and the number of samples in model learning.

Quantum Computing is an emerging paradigm which is gathering a lot of popularity in the current scientific and technological community. Widely conceived as the next frontier of computation, Quantum Computing is still at the dawn of its development being current solving systems suffering from significant limitations in terms of performance and capabilities. Some interesting approaches have been devised by researchers and practitioners in order to overcome these barriers, being quantum-classical hybrid algorithms one of the most often used solving schemes. The main goal of this paper is to extend the results and findings of the recently proposed hybrid Quantum Computing - Tabu Search Algorithm for partitioning problems. To do that, we focus our research on the adaptation of this method to the Asymmetric Traveling Salesman Problem. In overall, we have employed six well-known instances belonging to TSPLIB to assess the performance of Quantum Computing - Tabu Search Algorithm in comparison to QBSolv -- a state-of-the-art decomposing solver. Furthermore, as an additional contribution, this work also supposes the first solver of the Asymmetric Traveling Salesman Problem using a Quantum Computing based method. Aiming to boost whole community's research in QC, we have released the project's repository as open source code for further application and improvements.