We investigate the performance of the standard Greedy algorithm for cardinality constrained maximization of non-submodular nondecreasing set functions. While there are strong theoretical guarantees on the performance of Greedy for maximizing submodular functions, there are few guarantees for non-submodular ones. However, Greedy enjoys strong empirical performance for many important non-submodular functions, e.g., the Bayesian A-optimality objective in experimental design. We prove theoretical guarantees supporting the empirical performance. Our guarantees are characterized by a combination of the (generalized) curvature $\alpha$ and the submodularity ratio $\gamma$. In particular, we prove that Greedy enjoys a tight approximation guarantee of $\frac{1}{\alpha}(1- e^{-\gamma\alpha})$ for cardinality constrained maximization. In addition, we bound the submodularity ratio and curvature for several important real-world objectives, including the Bayesian A-optimality objective, the determinantal function of a square submatrix and certain linear programs with combinatorial constraints. We experimentally validate our theoretical findings for both synthetic and real-world applications.

In recent years, state-of-the-art game-playing agents often involve policies that are trained in self-playing processes where Monte Carlo tree search (MCTS) algorithms and trained policies iteratively improve each other. The strongest results have been obtained when policies are trained to mimic the search behaviour of MCTS by minimising a cross-entropy loss. Because MCTS, by design, includes an element of exploration, policies trained in this manner are also likely to exhibit a similar extent of exploration. In this paper, we are interested in learning policies for a project with future goals including the extraction of interpretable strategies, rather than state-of-the-art game-playing performance. For these goals, we argue that such an extent of exploration is undesirable, and we propose a novel objective function for training policies that are not exploratory. We derive a policy gradient expression for maximising this objective function, which can be estimated using MCTS value estimates, rather than MCTS visit counts. We empirically evaluate various properties of resulting policies, in a variety of board games.

Machine learning applied to architecture design presents a promising opportunity with broad applications. Recent deep reinforcement learning (DRL) techniques, in particular, enable efficient exploration in vast design spaces where conventional design strategies may be inadequate. This paper proposes a novel deep reinforcement framework, taking routerless networks-on-chip (NoC) as an evaluation case study. The new framework successfully resolves problems with prior design approaches being either unreliable due to random searches or inflexible due to severe design space restrictions. The framework learns (near-)optimal loop placement for routerless NoCs with various design constraints. A deep neural network is developed using parallel threads that efficiently explore the immense routerless NoC design space with a Monte Carlo search tree. Experimental results show that, compared with conventional mesh, the proposed deep reinforcement learning (DRL) routerless design achieves a 3.25x increase in throughput, 1.6x reduction in packet latency, and 5x reduction in power. Compared with the state-of-the-art routerless NoC, DRL achieves a 1.47x increase in throughput, 1.18x reduction in packet latency, and 1.14x reduction in average hop count albeit with slightly more power overhead.

State-of-the-art approaches to partially observable planning like POMCP are based on stochastic tree search. While these approaches are computationally efficient, they may still construct search trees of considerable size, which could limit the performance due to restricted memory resources. In this paper, we propose Partially Observable Stacked Thompson Sampling (POSTS), a memory bounded approach to open-loop planning in large POMDPs, which optimizes a fixed size stack of Thompson Sampling bandits. We empirically evaluate POSTS in four large benchmark problems and compare its performance with different tree-based approaches. We show that POSTS achieves competitive performance compared to tree-based open-loop planning and offers a performance-memory tradeoff, making it suitable for partially observable planning with highly restricted computational and memory resources.

Pattern analysis often requires a pre-processing stage for extracting or selecting features in order to help the classification, prediction, or clustering stage discriminate or represent the data in a better way. The reason for this requirement is that the raw data are complex and difficult to process without extracting or selecting appropriate features beforehand. This paper reviews theory and motivation of different common methods of feature selection and extraction and introduces some of their applications. Some numerical implementations are also shown for these methods. Finally, the methods in feature selection and extraction are compared.

We propose novel algorithms for design and design space exploration. The designs computed by these algorithms are compositions of function types specified in component libraries. Our algorithms reduce the design problem to quantified satisfiability and use advanced solvers to find solutions that represent useful systems. The algorithms we present in this paper are sound and complete and are guaranteed to discover correct designs of optimal size, if they exist. We apply our method to the design of Boolean systems and discover new and more optimal classical and quantum circuits for common arithmetic functions such as addition and multiplication. The performance of our algorithms is evaluated through extensive experimentation. We have first created a benchmark consisting of specifications of scalable synthetic digital circuits and real-world mirochips. We have then generated multiple circuits functionally equivalent to the ones in the benchmark. The quantified satisfiability method shows more than four orders of magnitude speed-up, compared to a generate and test method that enumerates all non-isomorphic circuit topologies. Our approach generalizes circuit optimization. It uses arbitrary component libraries and has applications to areas such as digital circuit design, diagnostics, abductive reasoning, test vector generation, and combinatorial optimization.

For network architecture search (NAS), it is crucial but challenging to simultaneously guarantee both effectiveness and efficiency. Towards achieving this goal, we develop a differentiable NAS solution, where the search space includes arbitrary feed-forward network consisting of the predefined number of connections. Benefiting from a proposed ensemble Gumbel-Softmax estimator, our method optimizes both the architecture of a deep network and its parameters in the same round of backward propagation, yielding an end-to-end mechanism of searching network architectures. Extensive experiments on a variety of popular datasets strongly evidence that our method is capable of discovering high-performance architectures, while guaranteeing the requisite efficiency during searching.

Nonconvex optimization is widely used in machine learning. Recently, for problems like matrix sensing (Bhojanapalli et al., 2016), matrix completion (Ge et al., 2016), and certain objectives for neural networks (Ge et al., 2017b), it was shown that all local minima are also globally optimal, therefore simple local search algorithms can be used to solve these problems. For a convex function f(x), a local and global minimum is achieved whenever the point has zero gradient: f(x) 0. However, for nonconvex functions, a point with zero gradient can also be a saddle point. To avoid converging to saddle points, recent results (Ge et al., 2015; Jin et al., 2017a,b) prove stronger results that show local search algorithms converge to ɛ-approximate second-order stationary points - points with small gradients and almost positive semi-definite Hessians (see Definition 1). In theory, Xu et al. (2018) and Allen-Zhu and Li (2017) independently showed that finding a second-order stationary point is not much harder than finding a first-order stationary point - they give reduction algorithms Neon/Neon2 that can converge to second-order stationary points when combined with algorithms that find first-order stationary points.

Data augmentation is an indispensable technique to improve generalization and also to deal with imbalanced datasets. Recently, AutoAugment (Cubuk et al., 2019) has been proposed to automatically search augmentation policies from a dataset and has significantly improved performances on many image recognition tasks. However, its search method requires thousands of GPU hours to train even in a reduced setting. In this paper, we propose Fast AutoAugment algorithm that learns augmentation policies using a more efficient search strategy based on density matching. In comparison to AutoAugment, the proposed algorithm speeds up the search time by orders of magnitude while maintaining the comparable performances on the image recognition tasks with various models and datasets including CIFAR-10, CIFAR-100, and ImageNet.

Interpretable classifiers have recently witnessed an increase in attention from the data mining community because they are inherently easier to understand and explain than their more complex counterparts. Examples of interpretable classification models include decision trees, rule sets, and rule lists. Learning such models often involves optimizing hyperparameters, which typically requires substantial amounts of data and may result in relatively large models. In this paper, we consider the problem of learning compact yet accurate probabilistic rule lists for multiclass classification. Specifically, we propose a novel formalization based on probabilistic rule lists and the minimum description length (MDL) principle. This results in virtually parameter-free model selection that naturally allows to trade-off model complexity with goodness of fit, by which overfitting and the need for hyperparameter tuning are effectively avoided. Finally, we introduce the Classy algorithm, which greedily finds rule lists according to the proposed criterion. We empirically demonstrate that Classy selects small probabilistic rule lists that outperform state-of-the-art classifiers when it comes to the combination of predictive performance and interpretability. We show that Classy is insensitive to its only parameter, i.e., the candidate set, and that compression on the training set correlates with classification performance, validating our MDL-based selection criterion.