We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires optimizing over a combinatorial space of program "architectures". We frame this optimization problem as a search in a weighted graph whose paths encode top-down derivations of program syntax. Our key innovation is to view various classes of neural networks as continuous relaxations over the space of programs, which can then be used to complete any partial program. This relaxed program is differentiable and can be trained end-to-end, and the resulting training loss is an approximately admissible heuristic that can guide the combinatorial search. We instantiate our approach on top of the A-star algorithm and an iteratively deepened branch-and-bound search, and use these algorithms to learn programmatic classifiers in three sequence classification tasks. Our experiments show that the algorithms outperform state-of-the-art methods for program learning, and that they discover programmatic classifiers that yield natural interpretations and achieve competitive accuracy.
AAC: Admissible-by-Architecture Differentiable Landmark Compression for ALT
Center for AI Research, VinUniversity, Vietnam（越南 Vin 大学人工智能研究中心）；VinRobotics, Vietnam（越南 Vin 机器人公司）；Intelligent Autonomous Systems, TU Darmstadt, Germany（德国图恩-达姆施塔特技术大学智能自主系统）
University of Denver（丹佛大学）；University of Alberta（阿尔伯塔大学）；University of Regina（里贾纳大学）
It is well-known that any admissible unidirectional heuristic search algorithm must expand all states whose $f$-value is smaller than the optimal solution cost when using a consistent heuristic. Such states are called "surely expanded" (s.e.). A recent study characterized s.e. pairs of states for bidirectional search with consistent heuristics: if a pair of states is s.e. then at least one of the two states must be expanded. This paper derives a lower bound, VC, on the minimum number of expansions required to cover all s.e. pairs, and present a new admissible front-to-end bidirectional heurist…
We present a heuristic search algorithm for solving first-order MDPs (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, we apply state abstraction directly on the FOMDP avoiding propositionalization. Such kind of abstraction is referred to as firstorder state abstraction. Secondly, guided by an admissible heuristic, the search is restricted only to those states that are reachable from the initial state. We demonstrate the usefullness of the above techniques for solving FOMDPs…
Queens College/City University of New York（纽约城市大学皇后学院）；Helsinki Institute for Information Technology（赫尔辛基信息技术研究所）；Mississippi State University（密西西比州立大学）
Recently two search algorithms, A* and breadth-first branch and bound (BFBnB), were developed based on a simple admissible heuristic for learning Bayesian network structures that optimize a scoring function. The heuristic represents a relaxation of the learning problem such that each variable chooses optimal parents independently. As a result, the heuristic may contain many directed cycles and result in a loose bound. This paper introduces an improved admissible heuristic that tries to avoid directed cycles within small groups of variables. A sparse representation is also introduced to store o…
NICTA（澳大利亚国家信息与通信技术研究院）；The Australian National University（澳大利亚国立大学）
The state of the art in local search for the Traveling Salesman Problem is dominated by ejection chain methods utilising the Stem-and-Cycle reference structure. Though effective such algorithms employ very little information in their successor selection strategy, typically seeking only to minimise the cost of a move. We propose an alternative approach inspired from the AI literature and show how an admissible heuristic can be used to guide successor selection. We undertake an empirical analysis and demonstrate that this technique often produces better results than less informed strategies albe…
International Center for Computational Logic（国际计算逻辑中心）；Technische Universität Dresden（德累斯顿工业大学）
We present a heuristic search algorithm for solving first-order Markov Decision Processes (FOMDPs). Our approach combines first-order state abstraction that avoids evaluating states individually, and heuristic search that avoids evaluating all states. Firstly, in contrast to existing systems, which start with propositionalizing the FOMDP and then perform state abstraction on its propositionalized version we apply state abstraction directly on the FOMDP avoiding propositionalization. This kind of abstraction is referred to as first-order state abstraction. Secondly, guided by an admissible heur…
Robotics Institute, Carnegie Mellon University（卡内基梅隆大学机器人研究所）
Heuristic search has traditionally relied on hand-crafted or programmatically derived heuristics. Neural networks (NNs) are newer powerful tools which can be used to learn complex mappings from states to cost-to-go heuristics. However, their slow single inference time is a large overhead that can substantially slow down planning time in optimized heuristic search implementations. Several recent works have described ways to take advantage of NN's batch computations to decrease overhead in planning, while retaining bounds on (sub)optimality. However, all these methods have used the NN heuristic …
NASA Ames Research Center（NASA艾姆斯研究中心）；LAAS-CNRS；Ben-Gurion University（本-古里安大学）；Mississippi State University（密西西比州立大学）；University of Washington（华盛顿大学）
We consider the problem of optimal planning in stochastic domains with resource constraints, where the resources are continuous and the choice of action at each step depends on resource availability. We introduce the HAO* algorithm, a generalization of the AO* algorithm that performs search in a hybrid state space that is modeled using both discrete and continuous state variables, where the continuous variables represent monotonic resources. Like other heuristic search algorithms, HAO* leverages knowledge of the start state and an admissible heuristic to focus computational effort on those par…
State-space search with explicit abstraction heuristics is at the state of the art of cost-optimal planning. These heuristics are inherently limited, nonetheless, because the size of the abstract space must be bounded by some, even if a very large, constant. Targeting this shortcoming, we introduce the notion of (additive) implicit abstractions, in which the planning task is abstracted by instances of tractable fragments of optimal planning. We then introduce a concrete setting of this framework, called fork-decomposition, that is based on two novel fragments of tractable cost-optimal planning…
Neural Module Network (NMN) is a machine learning model for solving the visual question answering tasks. NMN uses programs to encode modules' structures, and its modularized architecture enables it to solve logical problems more reasonably. However, because of the non-differentiable procedure of module selection, NMN is hard to be trained end-to-end. To overcome this problem, existing work either included ground-truth program into training data or applied reinforcement learning to explore the program. However, both of these methods still have weaknesses. In consideration of this, we proposed a…
In this paper, we address the problem of generating preferred plans by combining the procedural control knowledge specified by Hierarchical Task Networks (HTNs) with rich qualitative user preferences. The outcome of our work is a language for specifyin user preferences, tailored to HTN planning, together with a provably optimal preference-based planner, HTNPLAN, that is implemented as an extension of SHOP2. To compute preferred plans, we propose an approach based on forward-chaining heuristic search. Our heuristic uses an admissible evaluation function measuring the satisfaction of preferences…
Optimization of heuristic functions for the A* algorithm, realized by deep neural networks, is usually done by minimizing square root loss of estimate of the cost to goal values. This paper argues that this does not necessarily lead to a faster search of A* algorithm since its execution relies on relative values instead of absolute ones. As a mitigation, we propose a L* loss, which upper-bounds the number of excessively expanded states inside the A* search. The L* loss, when used in the optimization of state-of-the-art deep neural networks for automated planning in maze domains like Sokoban an…
Recently, the trend of incorporating differentiable algorithms into deep learning architectures arose in machine learning research, as the fusion of neural layers and algorithmic layers has been beneficial for handling combinatorial data, such as shortest paths on graphs. Recent works related to data-driven planning aim at learning either cost functions or heuristic functions, but not both. We propose Neural Weighted A*, a differentiable anytime planner able to produce improved representations of planar maps as graph costs and heuristics. Training occurs end-to-end on raw images with direct su…
Offline reinforcement learning, which aims at optimizing sequential decision-making strategies with historical data, has been extensively applied in real-life applications. State-Of-The-Art algorithms usually leverage powerful function approximators (e.g. neural networks) to alleviate the sample complexity hurdle for better empirical performances. Despite the successes, a more systematic understanding of the statistical complexity for function approximation remains lacking. Towards bridging the gap, we take a step by considering offline reinforcement learning with differentiable function class…
There has been a large literature of neural architecture search, but most existing work made use of heuristic rules that largely constrained the search flexibility. In this paper, we first relax these manually designed constraints and enlarge the search space to contain more than $10^{160}$ candidates. In the new space, most existing differentiable search methods can fail dramatically. We then propose a novel algorithm named Gradual One-Level Differentiable Neural Architecture Search (GOLD-NAS) which introduces a variable resource constraint to one-level optimization so that the weak operators…
In the last few years, artistic image-making with deep learning models has gained a considerable amount of traction. A large number of these models operate directly in the pixel space and generate raster images. This is however not how most humans would produce artworks, for example, by planning a sequence of shapes and strokes to draw. Recent developments in deep learning methods help to bridge the gap between stroke-based paintings and pixel photo generation. With this survey, we aim to provide a structured introduction and understanding of common challenges and approaches in stroke-based re…
In this paper we propose a novel network adaption method called Differentiable Network Adaption (DNA), which can adapt an existing network to a specific computation budget by adjusting the width and depth in a differentiable manner. The gradient-based optimization allows DNA to achieve an automatic optimization of width and depth rather than previous heuristic methods that heavily rely on human priors. Moreover, we propose a new elastic search space that can flexibly condense or expand during the optimization process, allowing the network optimization of width and depth in a bi-direction manne…
Differentiable Quadratic Optimization For The Maximum Independent Set Problem
University of Michigan, Ann Arbor（密歇根大学安娜堡分校）；Michigan State University（密歇根州立大学）；Ohio State University（俄亥俄州立大学）；University of Maryland, College Park（马里兰大学学院市分校）；University of Colorado, Boulder（科罗拉多大学博尔德分校）
本文提出 pCQO-MIS，通过融合最大团项的可微二次优化、并行动量梯度下降及理论驱动的 MIS 检查来求解最大独立集，在规模、运行时间和数据依赖方面优于多类方法。
Virtual Vehicle Research Center（虚拟车辆研究中心）；AVL List GmbH（AVL李斯特有限公司）；University of Sarajevo（萨拉热窝大学）
Planning and Learning are complementary approaches. Planning relies on deliberative reasoning about the current state and sequence of future reachable states to solve the problem. Learning, on the other hand, is focused on improving system performance based on experience or available data. Learning to improve the performance of planning based on experience in similar, previously solved problems, is ongoing research. One approach is to learn Value function (cost-to-go) which can be used as heuristics for speeding up search-based planning. Existing approaches in this direction use the results of…
We demonstrate the first Recurrent Neural Network architecture for learning Signal Temporal Logic formulas, and present the first systematic comparison of formula inference methods. Legacy systems embed much expert knowledge which is not explicitly formalized. There is great interest in learning formal specifications that characterize the ideal behavior of such systems -- that is, formulas in temporal logic that are satisfied by the system's output signals. Such specifications can be used to better understand the system's behavior and improve design of its next iteration. Previous inference me…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Adobe Research（Adobe 研究院）
In sequential recommender system applications, it is important to develop models that can capture users' evolving interest over time to successfully recommend future items that they are likely to interact with. For users with long histories, typical models based on recurrent neural networks tend to forget important items in the distant past. Recent works have shown that storing a small sketch of past items can improve sequential recommendation tasks. However, these works all rely on static sketching policies, i.e., heuristics to select items to keep in the sketch, which are not necessarily opt…
Bridging Arbitrary and Tree Metrics via Differentiable Gromov Hyperbolicity
Université Bretagne Sud IRISA, UMR 6074, CNRS（勃艮第大学 IRISA 实验室，UMR 6074，CNRS）；Université de Rennes IRMAR, UMR 6625, CNRS（雷恩大学 IRMAR 实验室，UMR 6625，CNRS）；L’Institut Agro Rennes-Angers IRISA, UMR 6074, CNRS（农业研究所雷恩-昂热 IRISA 实验室，UMR 6074，CNRS）；INRIA, ENS de Lyon, CNRS, Université Claude Bernard Lyon 1 LIP, UMR 5668（INRIA，里昂大学，CNRS，里昂第一大学 LIP 实验室，UMR 5668）
University of Central Florida（中佛罗里达大学）；Air Force Research Laboratory（空军研究实验室）
The success of machine learning solutions for reasoning about discrete structures has brought attention to its adoption within combinatorial optimization algorithms. Such approaches generally rely on supervised learning by leveraging datasets of the combinatorial structures of interest drawn from some distribution of problem instances. Reinforcement learning has also been employed to find such structures. In this paper, we propose a radically different approach in that no data is required for training the neural networks that produce the solution. In particular, we reduce the combinatorial opt…
Latent factor models are the driving forces of the state-of-the-art recommender systems, with an important insight of vectorizing raw input features into dense embeddings. The dimensions of different feature embeddings are often set to a same value empirically, which limits the predictive performance of latent factor models. Existing works have proposed heuristic or reinforcement learning-based methods to search for mixed feature embedding dimensions. For efficiency concern, these methods typically choose embedding dimensions from a restricted set of candidate dimensions. However, this restric…
Physics-informed Neural Networks (PINNs) have been widely used to obtain accurate neural surrogates for a system of Partial Differential Equations (PDE). One of the major limitations of PINNs is that the neural solutions are challenging to interpret, and are often treated as black-box solvers. While Symbolic Regression (SR) has been studied extensively, very few works exist which generate analytical expressions to directly perform SR for a system of PDEs. In this work, we introduce an end-to-end framework for obtaining mathematical expressions for solutions of PDEs. We use a trained PINN to ge…
GLL: A Differentiable Graph Learning Layer for Neural Networks
Department of Mathematics University of California, Los Angeles（数学系，加州大学洛杉矶分校）；Computing + Mathematical Sciences (CMS) Department California Institute of Technology（计算与数学科学系（CMS），加州理工学院）；School of Mathematics University of Minnesota（数学系，明尼苏达大学）
Learning to Approximate Uniform Facility Location via Graph Neural Networks
RWTH Aachen University, Germany（亚琛工业大学，德国）；Technical University of Munich, Germany（慕尼黑技术大学，德国）；Massachusetts Institute of Technology, USA（麻省理工学院，美国）；University of Cologne, Germany（科隆大学，德国）
