Retrosynthetic planning is a critical task in organic chemistry which identifies a series of reactions that can lead to the synthesis of a target product. The vast number of possible chemical transformations makes the size of the search space very big, and retrosynthetic planning is challenging even for experienced chemists. However, existing methods either require expensive return estimation by rollout with high variance, or optimize for search speed rather than the quality. In this paper, we propose Retro*, a neural-based A*-like algorithm that finds high-quality synthetic routes efficiently. It maintains the search as an AND-OR tree, and learns a neural search bias with off-policy data. Then guided by this neural network, it performs best-first search efficiently during new planning episodes. Experiments on benchmark USPTO datasets show that, our proposed method outperforms existing state-of-the-art with respect to both the success rate and solution quality, while being more efficient at the same time.

Many non-trivial sequential decision-making problems are efficiently solved by relying on Bellman's optimality principle, i.e., exploiting the fact that sub-problems are nested recursively within the original problem. Here we show how it can apply to (infinite horizon) 2-player zero-sum partially observable stochastic games (zs-POSGs) by (i) taking a central planner's viewpoint, which can only reason on a sufficient statistic called occupancy state, and (ii) turning such problems into zero-sum occupancy Markov games (zs-OMGs). Then, exploiting the Lipschitz-continuity of the value function in occupancy space, one can derive a version of the HSVI algorithm (Heuristic Search Value Iteration) that provably finds an $\epsilon$-Nash equilibrium in finite time.

Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such as stochastic gradient descent have become popular in practice. In this paper, we characterize the optimization landscape of the Tucker decomposition problem. In particular, we show that if the tensor has an exact Tucker decomposition, for a standard nonconvex objective of Tucker decomposition, all local minima are also globally optimal. We also give a local search algorithm that can find an approximate local (and global) optimal solution in polynomial time.

In this paper we propose a variant of the linear least squares model allowing practitioners to partition the input features into groups of variables that they require to contribute similarly to the final result. The output allows practitioners to assess the importance of each group and of each variable in the group. We formally show that the new formulation is not convex and provide two alternative methods to deal with the problem: one non-exact method based on an alternating least squares approach; and one exact method based on a reformulation of the problem using an exponential number of sub-problems whose minimum is guaranteed to be the optimal solution. We formally show the correctness of the exact method and also compare the two solutions showing that the exact solution provides better results in a fraction of the time required by the alternating least squares solution (assuming that the number of partitions is small). For the sake of completeness, we also provide an alternative branch and bound algorithm that can be used in place of the exact method when the number of partitions is too large, and a proof of NP-completeness of the optimization problem introduced in this paper.

Given a deep neural network image classification model that we treat as a black box, and an unlabeled evaluation dataset, we develop an efficient strategy by which the classifier can be evaluated. Randomly sampling and labeling instances from an unlabeled evaluation dataset allows traditional performance measures like accuracy, precision, and recall to be estimated. However, random sampling may miss rare errors for which the model is highly confident in its prediction, but wrong. These high-confidence errors can represent costly mistakes, and therefore should be explicitly searched for. Past works have developed search techniques to find classification errors above a specified confidence threshold, but ignore the fact that errors should be expected at confidence levels anywhere below 100\%. In this work, we investigate the problem of finding errors at rates greater than expected given model confidence. Additionally, we propose a query-efficient and novel search technique that is guided by adversarial perturbations to find these mistakes in black box models. Through rigorous empirical experimentation, we demonstrate that our Adversarial Distance search discovers high-confidence errors at a rate greater than expected given model confidence.

The Traveling Salesperson Problem (TSP) is a classical N P-hard optimization problem of utmost relevance, e.g., in transportation logistics, bioinformatics or circuit board fabrication. The goal is to route a salesperson through a set of cities such that each city is visited exactly once and the tour is of minimal length. In the past decades tremendous progress has been made in the development of high-performing heuristic TSP solvers. The local search-based Lin-Kernigham Heuristic (LKH) [14] and the genetic algorithm Edge-Assembly-Crossover (EAX) [35], along with their respective restart versions introduced in Kotthoff et al. [25], undeniably pose the state-of-the-art in inexact TSP solving. Automated Algorithm Selection (AS), originally proposed by Rice [39] back in 1976, is a powerful framework to predict the best-performing solver(s) from a portfolio of candidate solvers by means of machine learning. It has been successfully applied to a wide spectrum of challenging optimization problems in both the combinatorial [24, 29, 30, 40, 48] and continuous domain [21, 4] with partly astonishing performance gains - see the recent survey by Kerschke et al. [19] for a comprehensive overview. In particular, the TSP was subject to several successful ASstudies [25, 20, 33, 34, 37] which exploited the complementary performance profiles of simple heuristics on the one hand and the state-of-the-art solvers LKH and EAX on classical TSP benchmark sets on the other hand.

Designing efficient algorithms for combinatorial optimization appears ubiquitously in various scientific fields. Recently, deep reinforcement learning (DRL) frameworks have gained considerable attention as a new approach: they can automate the design of a solver while relying less on sophisticated domain knowledge of the target problem. However, the existing DRL solvers determine the solution using a number of stages proportional to the number of elements in the solution, which severely limits their applicability to large-scale graphs. In this paper, we seek to resolve this issue by proposing a novel DRL scheme, coined learning what to defer (LwD), where the agent adaptively shrinks or stretch the number of stages by learning to distribute the element-wise decisions of the solution at each stage. We apply the proposed framework to the maximum independent set (MIS) problem, and demonstrate its significant improvement over the current state-of-the-art DRL scheme. We also show that LwD can outperform the conventional MIS solvers on large-scale graphs having millions of vertices, under a limited time budget.

Rich user behavior data has been proven to be of great value for click-through rate prediction tasks, especially in industrial applications such as recommender systems and online advertising. Both industry and academy have paid much attention to this topic and propose different approaches to modeling with long sequential user behavior data. Among them, memory network based model MIMN proposed by Alibaba, achieves SOTA with the co-design of both learning algorithm and serving system. MIMN is the first industrial solution that can model sequential user behavior data with length scaling up to 1000. However, MIMN fails to precisely capture user interests given a specific candidate item when the length of user behavior sequence increases further, say, by 10 times or more. This challenge exists widely in previously proposed approaches. In this paper, we tackle this problem by designing a new modeling paradigm, which we name as Search-based Interest Model (SIM). SIM extracts user interests with two cascaded search units: (i) General Search Unit acts as a general search from the raw and arbitrary long sequential behavior data, with query information from candidate item, and gets a Sub user Behavior Sequence which is relevant to candidate item; (ii) Exact Search Unit models the precise relationship between candidate item and SBS. This cascaded search paradigm enables SIM with a better ability to model lifelong sequential behavior data in both scalability and accuracy. Apart from the learning algorithm, we also introduce our hands-on experience on how to implement SIM in large scale industrial systems. Since 2019, SIM has been deployed in the display advertising system in Alibaba, bringing 7.1\% CTR and 4.4\% RPM lift, which is significant to the business. Serving the main traffic in our real system now, SIM models user behavior data with maximum length reaching up to 54000, pushing SOTA to 54x.

Retrieving relevant targets from an extremely large target set under computational limits is a common challenge for information retrieval and recommendation systems. Tree models, which formulate targets as leaves of a tree with trainable node-wise scorers, have attracted a lot of interests in tackling this challenge due to their logarithmic computational complexity in both training and testing. Tree-based deep models (TDMs) and probabilistic label trees (PLTs) are two representative kinds of them. Though achieving many practical successes, existing tree models suffer from the training-testing discrepancy, where the retrieval performance deterioration caused by beam search in testing is not considered in training. This leads to an intrinsic gap between the most relevant targets and those retrieved by beam search with even the optimally trained node-wise scorers. We take a first step towards understanding and analyzing this problem theoretically, and develop the concept of Bayes optimality under beam search and calibration under beam search as general analyzing tools for this purpose. Moreover, to eliminate the discrepancy, we propose a novel algorithm for learning optimal tree models under beam search. Experiments on both synthetic and real data verify the rationality of our theoretical analysis and demonstrate the superiority of our algorithm compared to state-of-the-art methods.

Methods for dynamic difficulty adjustment allow games to be tailored to particular players to maximize their engagement. However, current methods often only modify a limited set of game features such as the difficulty of the opponents, or the availability of resources. Other approaches, such as experience-driven Procedural Content Generation (PCG), can generate complete levels with desired properties such as levels that are neither too hard nor too easy, but require many iterations. This paper presents a method that can generate and search for complete levels with a specific target difficulty in only a few trials. This advance is enabled by through an Intelligent Trial-and-Error algorithm, originally developed to allow robots to adapt quickly. Our algorithm first creates a large variety of different levels that vary across predefined dimensions such as leniency or map coverage. The performance of an AI playing agent on these maps gives a proxy for how difficult the level would be for another AI agent (e.g. one that employs Monte Carlo Tree Search instead of Greedy Tree Search); using this information, a Bayesian Optimization procedure is deployed, updating the difficulty of the prior map to reflect the ability of the agent. The approach can reliably find levels with a specific target difficulty for a variety of planning agents in only a few trials, while maintaining an understanding of their skill landscape.