We consider the problem of learning optimal binary classification trees. Literature on the topic has burgeoned in recent years, motivated both by the empirical suboptimality of heuristic approaches and the tremendous improvements in mixed-integer programming (MIP) technology. Yet, existing approaches from the literature do not leverage the power of MIP to its full extent. Indeed, they rely on weak formulations, resulting in slow convergence and large optimality gaps. To fill this gap in the literature, we propose a flow-based MIP formulation for optimal binary classification trees that has a stronger linear programming relaxation. Our formulation presents an attractive decomposable structure. We exploit this structure and max-flow/min-cut duality to derive a Benders' decomposition method, which scales to larger instances. We conduct extensive computational experiments on standard benchmark datasets on which we show that our proposed approaches are 50 times faster than state-of-the art MIP-based techniques and improve out of sample performance up to 13.8%.

Sampling is a fundamental technique, and sampling without replacement is often desirable when duplicate samples are not beneficial. Within machine learning, sampling is useful for generating diverse outputs from a trained model. We present an elegant procedure for sampling without replacement from a broad class of randomized programs, including generative neural models that construct outputs sequentially. Our procedure is efficient even for exponentially-large output spaces. Unlike prior work, our approach is incremental, i.e., samples can be drawn one at a time, allowing for increased flexibility. We also present a new estimator for computing expectations from samples drawn without replacement. We show that incremental sampling without replacement is applicable to many domains, e.g., program synthesis and combinatorial optimization.

Detecting the Maximum Common Subgraph (MCS) between two input graphs is fundamental for applications in biomedical analysis, malware detection, cloud computing, etc. This is especially important in the task of drug design, where the successful extraction of common substructures in compounds can reduce the number of experiments needed to be conducted by humans. However, MCS computation is NP-hard, and state-of-the-art exact MCS solvers do not have worst-case time complexity guarantee and cannot handle large graphs in practice. Designing learning based models to find the MCS between two graphs in an approximate yet accurate way while utilizing as few labeled MCS instances as possible remains to be a challenging task. Here we propose RLMCS, a Graph Neural Network based model for MCS detection through reinforcement learning. Our model uses an exploration tree to extract subgraphs in two graphs one node pair at a time, and is trained to optimize subgraph extraction rewards via Deep Q-Networks. A novel graph embedding method is proposed to generate state representations for nodes and extracted subgraphs jointly at each step. Experiments on real graph datasets demonstrate that our model performs favorably to exact MCS solvers and supervised neural graph matching network models in terms of accuracy and efficiency.

Cyber-attacks can occur at machine speeds that are far too fast for human-in-the-loop (or sometimes on-the-loop) decision making to be a viable option. Although human inputs are still important, a defensive Artificial Intelligence (AI) system must have considerable autonomy in these circumstances. When the AI system is model-based, its behavior responses can be aligned with risk-aware cost/benefit tradeoffs that are defined by user-supplied preferences that capture the key aspects of how human operators understand the system, the adversary and the mission. This paper describes an approach to automated cyber response that is designed along these lines. We combine a simulation of the system to be defended with an anytime online planner to solve cyber defense problems characterized as partially observable Markov decision problems (POMDPs).

Automatic surgical gesture recognition is fundamental for improving intelligence in robot-assisted surgery, such as conducting complicated tasks of surgery surveillance and skill evaluation. However, current methods treat each frame individually and produce the outcomes without effective consideration on future information. In this paper, we propose a framework based on reinforcement learning and tree search for joint surgical gesture segmentation and classification. An agent is trained to segment and classify the surgical video in a human-like manner whose direct decisions are re-considered by tree search appropriately. Our proposed tree search algorithm unites the outputs from two designed neural networks, i.e., policy and value network. With the integration of complementary information from distinct models, our framework is able to achieve the better performance than baseline methods using either of the neural networks. For an overall evaluation, our developed approach consistently outperforms the existing methods on the suturing task of JIGSAWS dataset in terms of accuracy, edit score and F1 score. Our study highlights the utilization of tree search to refine actions in reinforcement learning framework for surgical robotic applications.

This paper presents an approach to learn the local-search heuristics that iteratively improves the solution of Vehicle Routing Problem (VRP). A local-search heuristics is composed of a destroy operator that destructs a candidate solution, and a following repair operator that rebuilds the destructed one into a new one. The proposed neural network, as trained through actor-critic framework, consists of an encoder in form of a modified version of Graph Attention Network where node embeddings and edge embeddings are integrated, and a GRU-based decoder rendering a pair of destroy and repair operators. Experiment results show that it outperforms both the traditional heuristics algorithms and the existing neural combinatorial optimization for VRP on medium-scale data set, and is able to tackle the large-scale data set (e.g., over 400 nodes) which is a considerable challenge in this area. Moreover, the need for expertise and handcrafted heuristics design is eliminated due to the fact that the proposed network learns to design the heuristics with a better performance. Our implementation is available online. 1 Keywords Vehicle Routing Problem · Combinatorial Optimization · Large Neighborhood Search · Neural Combinatorial Search · Reinforcement Learning · Graph Attention Network

We give a local search based algorithm for $k$-median ($k$-means) clustering from the perspective of individual fairness. More precisely, for a point $x$ in a point set $P$ of size $n$, let $r(x)$ be the minimum radius such that the ball of radius $r(x)$ centered at $x$ has at least $n/k$ points from $P$. Intuitively, if a set of $k$ random points are chosen from $P$ as centers, every point $x\in P$ expects to have a center within radius $r(x)$. An individually fair clustering provides such a guarantee for every point $x\in P$. This notion of fairness was introduced in [Jung et al., 2019] where they showed how to get an approximately feasible $k$-clustering with respect to this fairness condition. In this work, we show how to get an approximately optimal such fair $k$-clustering. The $k$-median ($k$-means) cost of our solution is within a constant factor of the cost of an optimal fair $k$-clustering, and our solution approximately satisfies the fairness condition (also within a constant factor). Further, we complement our theoretical bounds with empirical evaluation.

This paper describes a recursive estimation procedure for multivariate binary densities using orthogonal expansions. For $d$ covariates, there are $2 d$ basis coefficients to estimate, which renders conventional approaches computationally prohibitive when $d$ is large. However, for a wide class of densities that satisfy a certain sparsity condition, our estimator runs in probabilistic polynomial time and adapts to the unknown sparsity of the underlying density in two key ways: (1) it attains near-minimax mean-squared error, and (2) the computational complexity is lower for sparser densities. Our method also allows for flexible control of the trade-off between mean-squared error and computational complexity. Papers published at the Neural Information Processing Systems Conference.

Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation that minimizes the maximum of the tasks' empirical risks. Via a certain relaxation of minimax MTL, we obtain a continuum of MTL formulations spanning minimax MTL and classical MTL. The full paradigm itself is loss-compositional, operating on the vector of empirical risks.

Monte-Carlo Tree Search (MCTS) has proven to be a powerful, generic planning technique for decision-making in single-agent and adversarial environments. The stochastic nature of the Monte-Carlo simulations introduces errors in the value estimates, both in terms of bias and variance. Whilst reducing bias (typically through the addition of domain knowledge) has been studied in the MCTS literature, comparatively little effort has focused on reducing variance. This is somewhat surprising, since variance reduction techniques are a well-studied area in classical statistics. In this paper, we examine the application of some standard techniques for variance reduction in MCTS, including common random numbers, antithetic variates and control variates.