Color refinement is a basic algorithmic routine for graph isomorphismtesting and has recently been used for computing graph kernels as well as for lifting belief propagation and linear programming. So far, color refinement has been treated as a combinatorial problem. Instead, we treat it as a nonlinear continuous optimization problem and prove thatit implements a conditional gradient optimizer that can be turned into graph clustering approaches using hashing and truncated power iterations. This shows that color refinement is easy to understand in terms of random walks, easy to implement (matrix-matrix/vector multiplications) and readily parallelizable. We support our theoretical results with experiments on real-world graphs with millions of edges.

During the past decade, machine learning algorithms have become commonplace in large-scale real-world industrial applications. In these settings, the computation time to train and test machine learning algorithms is a key consideration. At training-time the algorithms must scale to very large data set sizes.At testing-time, the cost of feature extraction can dominate the CPU runtime. Recently, a promising method was proposed to account for the feature extraction cost at testing time, called Cost-sensitive Tree of Classifiers (CSTC). Although the CSTC problem is NP-hard, the authors suggest an approximation through a mixed-norm relaxation across many classifiers. This relaxation is slow to train and requires involved optimization hyperparameter tuning. We propose a different relaxation using approximate submodularity, called Approximately Submodular Tree of Classifiers (ASTC). ASTC is much simpler to implement, yields equivalent results but requires no optimization hyperparameter tuning and is up to two orders of magnitude faster to train.

Sparse modeling has been highly successful in many real-world applications. While a lot of interests have been on convex regularization, recent studies show that nonconvexregularizers can outperform their convex counterparts in many situations.However, the resulting nonconvex optimization problems are often challenging, especiallyfor composite regularizers such as the nonconvex overlapping group lasso. In thispaper, byusing a recent mathematical tool known as the proximal average,we propose a novel proximal gradient descent method for optimization with a wide class of nonconvex and composite regularizers.Instead of directlysolving the proximal stepassociated with a composite regularizer, we average thesolutions from the proximal problems of the constituent regularizers. This simple strategy has guaranteed convergenceand low per-iteration complexity.Experimental results on a number of synthetic andreal-world data sets demonstrate the effectiveness and efficiency of theproposed optimization algorithm, and also the improved classification performanceresulting from thenonconvex regularizers.

We present a ping-pong-playing robot that learns to improve its swings with human advice. Our method learns a reward function over the joint space of task and policy parameters T×P, so the robot can explore policy space more intelligently in a way that trades off exploration vs. exploitation to maximize the total cumulative reward over time. Multimodal stochastic polices can also easily be learned with this approach when the reward function is multimodal in the policy parameters. We extend the recently-developed Gaussian Process Bandit Optimization framework to include exploration-bias advice from human domain experts, using a novel algorithm called Exploration Bias with Directional Advice (EBDA).

Choice selection processes are a family of bilateral games of incomplete information in which a computer agent generates advice for a human user while considering the effect of the advice on the user's behavior in future interactions. The human and the agent may share certain goals, but are essentially self-interested. This paper extends selection processes to settings in which the actions available to the human are ordered and thus the user may be influenced by the advice even though he doesn't necessarily follow it exactly. In this work we also consider the case in which the user obtains some observation on the sate of the world. We propose several approaches to model human decision making in such settings. We incorporate these models into two optimization techniques for the agent advice provision strategy. In the first one the agent used a social utility approach which considered the benefits and costs for both agent and person when making suggestions. In the second approach we simplified the human model in order to allow modeling and solving the agent strategy as an MDP. In an empirical evaluation involving human users on AMT, we showed that the social utility approach significantly outperformed the MDP approach.

We present a novel approach to low-dimensional neighbor embedding for visualization, based on formulating an information retrieval based neighborhood preservation cost function as Maximum satisfiability on a discretized output display. The method has a rigorous interpretation as optimal visualization based on the cost function. Unlike previous low-dimensional neighbor embedding methods, our formulation is guaranteed to yield globally optimal visualizations, and does so reasonably fast. Unlike previous manifold learning methods yielding global optima of their cost functions, our cost function and method are designed for low-dimensional visualization where evaluation and minimization of visualization errors are crucial. Our method performs well in experiments, yielding clean embeddings of datasets where a state-of-the-art comparison method yields poor arrangements. In a real-world case study for semi-supervised WLAN signal mapping in buildings we outperform state-of-the-art methods.

A wide range of robotic missions contain actions that exhibit looping behavior. Examples of these actions include picking fruit in agriculture, pick-and-place tasks in manufacturing and search patterns in robotic search or survey missions. These looping actions often have a range of acceptable values for the number of loops and a preference function over them. For example, during robotic survey missions, the information gain is expected to increase with the number of loops in a search pattern. Since these looping actions also take time, which is typically bounded, there is a challenge of maximizing utility while respecting time constraints. In this paper, we introduce the Looping Temporal Problem with Preference (LTPP) as a simple parameterized extension of a simple temporal problem. In addition, we introduce a scheduling algorithm for LTPPs which leverages the structure of the problem to find the optimal solution efficiently. We show more than an order of magnitude improvement in run-time over current scheduling techniques and framing a LTPP as a MINLP.

Imitation Learning (IL) is a popular approach for teaching behavior policies to agents by demonstrating the desired target policy. While the approach has lead to many successes, IL often requires a large set of demonstrations to achieve robust learning, which can be expensive for the teacher. In this paper, we consider a novel approach to improve the learning efficiency of IL by providing a shaping reward function in addition to the usual demonstrations. Shaping rewards are numeric functions of states (and possibly actions) that are generally easily specified, and capture general principles of desired behavior, without necessarily completely specifying the behavior. Shaping rewards have been used extensively in reinforcement learning, but have been seldom considered for IL, though they are often easy to specify. Our main contribution is to propose an IL approach that learns from both shaping rewards and demonstrations. We demonstrate the effectiveness of the approach across several IL problems, even when the shaping reward is not fully consistent with the demonstrations.

In this paper, we solve cooperative decentralized stochastic planning problems, where the interactions between agents (specified using transition and reward functions) are dependent on the number of agents (and not on the identity of the individual agents) involved in the interaction. A collision of robots in a narrow corridor, defender teams coordinating patrol activities to secure a target, etc. are examples of such anonymous interactions. Formally, we consider problems that are a subset of the well known Decentralized MDP (DEC-MDP) model, where the anonymity in interactions is specified within the joint reward and transition functions. In this paper, not only do we introduce a general model model called D-SPAIT to capture anonymity in interactions, but also provide optimization based optimal and local-optimal solutions for generalizable sub-categories of D-SPAIT.

Hashing has recently attracted considerable attention for large scale similarity search. However, learning compact codes with good performance is still a challenge. In many cases, the real-world data lies on a low-dimensional manifold embedded in high-dimensional ambient space. To capture meaningful neighbors, a compact hashing representation should be able to uncover the intrinsic geometric structure of the manifold, e.g., the neighborhood relationships between subregions. Most existing hashing methods only consider this issue during mapping data points into certain projected dimensions. When getting the binary codes, they either directly quantize the projected values with a threshold, or use an orthogonal matrix to refine the initial projection matrix, which both consider projection and quantization separately, and will not well preserve the locality structure in the whole learning process. In this paper, we propose a novel hashing algorithm called Locality Preserving Hashing to effectively solve the above problems. Specifically, we learn a set of locality preserving projections with a joint optimization framework, which minimizes the average projection distance and quantization loss simultaneously. Experimental comparisons with other state-of-the-art methods on two large scale datasets demonstrate the effectiveness and efficiency of our method.