The performance of trained neural networks is robust to harsh levels of pruning. Coupled with the ever-growing size of deep learning models, this observation has motivated extensive research on learning sparse models. In this work, we focus on the task of controlling the level of sparsity when performing sparse learning. Existing methods based on sparsity-inducing penalties involve expensive trial-and-error tuning of the penalty factor, thus lacking direct control of the resulting model sparsity. In response, we adopt a constrained formulation: using the gate mechanism proposed by Louizos et al. (2018), we formulate a constrained optimization problem where sparsification is guided by the training objective and the desired sparsity target in an end-to-end fashion.

We study the problem of learning a linear model to set the reserve price in an auction, given contextual information, in order to maximize expected revenue from the seller side. First, we show that it is not possible to solve this problem in polynomial time unless the Exponential Time Hypothesis fails. Second, we present a strong mixed-integer programming (MIP) formulation for this problem, which is capable of exactly modeling the nonconvex and discontinuous expected reward function. Moreover, we show that this MIP formulation is ideal (i.e. the strongest possible formulation) for the revenue function of a single impression. Since it can be computationally expensive to exactly solve the MIP formulation in practice, we also study the performance of its linear programming (LP) relaxation. Though it may work well in practice, we show that, unfortunately, in the worst case the optimal objective of the LP relaxation can be O(number of samples) times larger than the optimal objective of the true problem.

Real-world decision-making systems are often subject to uncertainties that have to be resolved through observational data. Therefore, we are frequently confronted with combinatorial optimization problems of which the objective function is unknown and thus has to be debunked using empirical evidence. In contrast to the common practice that relies on a learning-and-optimization strategy, we consider the regression between combinatorial spaces, aiming to infer high-quality optimization solutions from samples of input-solution pairs -- without the need to learn the objective function. Our main deliverable is a universal solver that is able to handle abstract undetermined stochastic combinatorial optimization problems. In empirical studies, we demonstrate our design using proof-of-concept experiments, and compare it with other methods that are potentially applicable. Overall, we obtain highly encouraging experimental results for several classic combinatorial problems on both synthetic and real-world datasets.

Boosting variational inference (BVI) approximates an intractable probability density by iteratively building up a mixture of simple component distributions one at a time, using techniques from sparse convex optimization to provide both computational scalability and approximation error guarantees. But the guarantees have strong conditions that do not often hold in practice, resulting in degenerate component optimization problems; and we show that the ad-hoc regularization used to prevent degeneracy in practice can cause BVI to fail in unintuitive ways. We thus develop universal boosting variational inference (UBVI), a BVI scheme that exploits the simple geometry of probability densities under the Hellinger metric to prevent the degeneracy of other gradient-based BVI methods, avoid difficult joint optimizations of both component and weight, and simplify fully-corrective weight optimizations. We show that for any target density and any mixture component family, the output of UBVI converges to the best possible approximation in the mixture family, even when the mixture family is misspecified. We develop a scalable implementation based on exponential family mixture components and standard stochastic optimization techniques.

We study the deterministic global optimization of the K-Medoids clustering problem. This work proposes a branch and bound (BB) scheme, in which a tailored Lagrangian relaxation method proposed in the 1970s is used to provide a lower bound at each BB node. The lower bounding method already guarantees the maximum gap at the root node. A closed-form solution to the lower bound can be derived analytically without explicitly solving any optimization problems, and its computation can be easily parallelized. Moreover, with this lower bounding method, finite convergence to the global optimal solution can be guaranteed by branching only on the regions of medoids. We also present several tailored bound tightening techniques to reduce the search space and computational cost.

It is well-known that given a smooth, bounded-from-below, and possibly nonconvex function, standard gradient-based methods can find \epsilon -stationary points (with gradient norm less than \epsilon) in \mathcal{O}(1/\epsilon 2) iterations. However, many important nonconvex optimization problems, such as those associated with training modern neural networks, are inherently not smooth, making these results inapplicable. In this paper, we study nonsmooth nonconvex optimization from an oracle complexity viewpoint, where the algorithm is assumed to be given access only to local information about the function at various points. We provide two main results (under mild assumptions): First, we consider the problem of getting \emph{near} \epsilon -stationary points. This is perhaps the most natural relaxation of \emph{finding} \epsilon -stationary points, which is impossible in the nonsmooth nonconvex case.

We developed a new method PROTES for black-box optimization, which is based on the probabilistic sampling from a probability density function given in the low-parametric tensor train format. We tested it on complex multidimensional arrays and discretized multivariable functions taken, among others, from real-world applications, including unconstrained binary optimization and optimal control problems, for which the possible number of elements is up to 2 {1000} . In numerical experiments, both on analytic model functions and on complex problems, PROTES outperforms popular discrete optimization methods (Particle Swarm Optimization, Covariance Matrix Adaptation, Differential Evolution, and others).

This is a great work as it tackles an important problem: graph partitioning in heterogeneous/multi-device settings. There is an increasing number of problems that could benefit from resource allocation optimization techniques such as the one described in this work. ML and specifically RL techniques have been recently developed to solve the problem of device placement. This work addresses one of the main deficiencies of the prior work by making more sample efficient (as demonstrated by empirical results). The novelty is in the way the placement parameters are trained: As oppose to directly train a placement policy for best runtime, a softmax is used to model the distribution of op placements on devices (for each device among the pool of available devices.)

We address a task of local trajectory planning for the mobile robot in the presence of static and dynamic obstacles. Local trajectory is obtained as a numerical solution of the Model Predictive Control (MPC) problem. Collision avoidance may be provided by adding repulsive potential of the obstacles to the cost function of MPC. We develop an approach, where repulsive potential is estimated by the neural model. We propose and explore three possible strategies of handling dynamic obstacles. First, environment with dynamic obstacles is considered as a sequence of static environments. Second, the neural model predict a sequence of repulsive potential at once. Third, the neural model predict future repulsive potential step by step in autoregressive mode. We implement these strategies and compare it with CIAO* and MPPI using BenchMR framework. First two strategies showed higher performance than CIAO* and MPPI while preserving safety constraints. The third strategy was a bit slower, however it still satisfy time limits. We deploy our approach on Husky UGV mobile platform, which move through the office corridors under proposed MPC local trajectory planner. The code and trained models are available at \url{https://github.com/CognitiveAISystems/Dynamic-Neural-Potential-Field}.

Dense Convolutional Network has been continuously refined to adopt a highly efficient and compact architecture, owing to its lightweight and efficient structure. However, the current Dense-like architectures are mainly designed manually, it becomes increasingly difficult to adjust the channels and reuse level based on past experience. As such, we propose an architecture search method called Dense Optimizer that can search high-performance dense-like network automatically. In Dense Optimizer, we view the dense network as a hierarchical information system, maximize the network's information entropy while constraining the distribution of the entropy across each stage via a power law, thereby constructing an optimization problem. We also propose a branch-and-bound optimization algorithm, tightly integrates power-law principle with search space scaling to solve the optimization problem efficiently. The superiority of Dense Optimizer has been validated on different computer vision benchmark datasets. Specifically, Dense Optimizer completes high-quality search but only costs 4 hours with one CPU. Our searched model DenseNet-OPT achieved a top 1 accuracy of 84.3% on CIFAR-100, which is 5.97% higher than the original one.