Allocating physical layer resources to users based on channel quality, buffer size, requirements and constraints represents one of the central optimization problems in the management of radio resources. The solution space grows combinatorially with the cardinality of each dimension making it hard to find optimal solutions using an exhaustive search or even classical optimization algorithms given the stringent time requirements. This problem is even more pronounced in MU-MIMO scheduling where the scheduler can assign multiple users to the same time-frequency physical resources. Traditional approaches thus resort to designing heuristics that trade optimality in favor of feasibility of execution. In this work we treat the MU-MIMO scheduling problem as a tree-structured combinatorial problem and, borrowing from the recent successes of AlphaGo Zero, we investigate the feasibility of searching for the best performing solutions using a combination of Monte Carlo Tree Search and Reinforcement Learning. To cater to the nature of the problem at hand, like the lack of an intrinsic ordering of the users as well as the importance of dependencies between combinations of users, we make fundamental modifications to the neural network architecture by introducing the self-attention mechanism. We then demonstrate that the resulting approach is not only feasible but vastly outperforms state-of-the-art heuristic-based scheduling approaches in the presence of measurement uncertainties and finite buffers.

We consider the problem of learning a sparse undirected graph underlying a given set of multivariate data. We focus on graph Laplacian-related constraints on the sparse precision matrix that encodes conditional dependence between the random variables associated with the graph nodes. Under these constraints the off-diagonal elements of the precision matrix are non-positive (total positivity), and the precision matrix may not be full-rank. We investigate modifications to widely used penalized log-likelihood approaches to enforce total positivity but not the Laplacian structure. The graph Laplacian can then be extracted from the off-diagonal precision matrix. An alternating direction method of multipliers (ADMM) algorithm is presented and analyzed for constrained optimization under Laplacian-related constraints and lasso as well as adaptive lasso penalties. Numerical results based on synthetic data show that the proposed constrained adaptive lasso approach significantly outperforms existing Laplacian-based approaches. We also evaluate our approach on real financial data.

Real-world content recommendation marketplaces exhibit certain behaviors and are imposed by constraints that are not always apparent in common static offline data sets. One example that is common in ad marketplaces is swift ad turnover. New ads are introduced and old ads disappear at high rates every day. Another example is ad discontinuity, where existing ads may appear and disappear from the market for non negligible amounts of time due to a variety of reasons (e.g., depletion of budget, pausing by the advertiser, flagging by the system, and more). These behaviors sometimes cause the model's loss surface to change dramatically over short periods of time. To address these behaviors, fresh models are highly important, and to achieve this (and for several other reasons) incremental training on small chunks of past events is often employed. These behaviors and algorithmic optimizations occasionally cause model parameters to grow uncontrollably large, or \emph{diverge}. In this work present a systematic method to prevent model parameters from diverging by imposing a carefully chosen set of constraints on the model's latent vectors. We then devise a method inspired by primal-dual optimization algorithms to fulfill these constraints in a manner which both aligns well with incremental model training, and does not require any major modifications to the underlying model training algorithm. We analyze, demonstrate, and motivate our method on OFFSET, a collaborative filtering algorithm which drives Yahoo native advertising, which is one of VZM's largest and faster growing businesses, reaching a run-rate of many hundreds of millions USD per year. Finally, we conduct an online experiment which shows a substantial reduction in the number of diverging instances, and a significant improvement to both user experience and revenue.

Taxicab service plays an essential and irreplaceable role in urban traffic system [Ji et al., 2020]. For example, in New York City, there are more than 21,000 taxi drivers and more than 80,000 ride-sharing drivers. Compared to other means of daily transportation, such as bus and subway, taxis usually offers a better trip experience in terms of comfort, convenience, and travel time accommodation. Thus, it has been a long-standing central issue to improve the efficiency of vehicle mobility by optimizing the route recommendation for drivers for taxi services in big cities like New York, Tokyo, and Beijing [Yuan et al., 2011, Zheng et al., 2014]. Based on large-scale taxi trace data, there is an extensive literature on route recommendation systems. Some studies focus on the traditional optimization method. For example, Qu et al. [2014] proposed a cost-efficient objective function and developed a greedy method to maximize the potential net profit. Similar methods can be found in [Ding et al., 2013, Zhou et al., 2016]. Stochastic optimization methods (e.g., simulated annealing -SA-) and parallel computing techniques have also been applied to route recommendation problems to speed up the route searching tasks (see [Ye This manuscript has been accepted by ACM Transactions on Intelligent Systems and Technology on April 25, 2021.

This article is a walkthrough to perform optimization on Pokemon data using PuLp, the linear programming and optimization library.

Optimization problems involve the identification of the best possible solution among several possibilities. These problems can be encountered in real-world settings, as well as in most scientific research fields. In recent years, computer scientists have developed increasingly advanced computational methods for solving optimization problems. Some of the most promising techniques developed so far are based on artificial neural networks (ANNs). Researchers at the Vector Institute, University of Waterloo and Perimeter Institute for Theoretical Physics in Canada have recently developed variational neural annealing, a new optimization method that merges recurrent neural networks (RNNs) with the principle of annealing.

Deep learning has seen a lot of recent success in tackling difficult problems that require extracting useful information from large amounts of data. Such work has shown promising results for learning difficult tasks in image recognition, natural language, time-series forecasting, etc. Traditionally, these networks have millions of parameters that are learned using an optimization algorithm. Optimization informs parameters how to update to capture features of the input relevant for learning the task at hand. While these models are often well suited for the tasks on which they are applied, they have not yet shown the ability to bootstrap a-priori knowledge for novel tasks. Even the limited approaches that show some transfer of previously learned knowledge don't scale, in terms of resources, in the same manner as seen in biological brains.

Vision-and-Language Navigation (VLN) is a task where an agent navigates in an embodied indoor environment under human instructions. Previous works ignore the distribution of sample difficulty and we argue that this potentially degrade their agent performance. To tackle this issue, we propose a novel curriculum-based training paradigm for VLN tasks that can balance human prior knowledge and agent learning progress about training samples. We develop the principle of curriculum design and re-arrange the benchmark Room-to-Room (R2R) dataset to make it suitable for curriculum training. Experiments show that our method is model-agnostic and can significantly improve the performance, the generalizability, and the training efficiency of current state-of-the-art navigation agents without increasing model complexity.

Recent studies have revealed that neural combinatorial optimization (NCO) has advantages over conventional algorithms in many combinatorial optimization problems such as routing, but it is less efficient for more complicated optimization tasks such as packing which involves mutually conditioned action spaces. In this paper, we propose a Recurrent Conditional Query Learning (RCQL) method to solve both 2D and 3D packing problems. We first embed states by a recurrent encoder, and then adopt attention with conditional queries from previous actions. The conditional query mechanism fills the information gap between learning steps, which shapes the problem as a Markov decision process. Benefiting from the recurrence, a single RCQL model is capable of handling different sizes of packing problems. Experiment results show that RCQL can effectively learn strong heuristics for offline and online strip packing problems (SPPs), outperforming a wide range of baselines in space utilization ratio. RCQL reduces the average bin gap ratio by 1.83% in offline 2D 40-box cases and 7.84% in 3D cases compared with state-of-the-art methods. Meanwhile, our method also achieves 5.64% higher space utilization ratio for SPPs with 1000 items than the state of the art.

In this note, we investigate how well we can reconstruct the best rank-$r$ approximation of a large matrix from a small number of its entries. We show that even if a data matrix is of full rank and cannot be approximated well by a low-rank matrix, its best low-rank approximations may still be reliably computed or estimated from a small number of its entries. This is especially relevant from a statistical viewpoint: the best low-rank approximations to a data matrix are often of more interest than itself because they capture the more stable and oftentimes more reproducible properties of an otherwise complicated data-generating model. In particular, we investigate two agnostic approaches: the first is based on spectral truncation; and the second is a projected gradient descent based optimization procedure. We argue that, while the first approach is intuitive and reasonably effective, the latter has far superior performance in general. We show that the error depends on how close the matrix is to being of low rank. Both theoretical and numerical evidence is presented to demonstrate the effectiveness of the proposed approaches.