We take initial steps in studying PAC-MDP algorithms with limited adaptivity, that is, algorithms that change its exploration policy as infrequently as possible during regret minimization. This is motivated by the difficulty of running fully adaptive algorithms in real-world applications (such as medical domains), and we propose to quantify adaptivity using the notion of local switching cost. Our main contribution, Q-Learning with UCB2 exploration, is a model-free algorithm for H-step episodic MDP that achieves sublinear regret whose local switching cost in K episodes is $O(H^3SA\log K)$, and we provide a lower bound of $\Omega(HSA)$ on the local switching cost for any no-regret algorithm. Our algorithm can be naturally adapted to the concurrent setting, which yields nontrivial results that improve upon prior work in certain aspects.

Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as high-low-level SVR approach (HL-SVR) is proposed for data modeling of input parameters of unequal sample sizes in this paper. The proposed approach is consisted of low-level SVR models for the input parameters of larger sample sizes and high-level SVR model for the input parameters of smaller sample sizes. For each training point of the input parameters of smaller sample sizes, one low-level SVR model is built based on its corresponding input parameters of larger sample sizes and their responses of interest. The high-level SVR model is built based on the obtained responses from the low-level SVR models and the input parameters of smaller sample sizes. Several numerical examples are used to validate the performance of HL-SVR. The experimental results indicate that HL-SVR can produce more accurate prediction results than conventional SVR. The proposed approach is applied on the stress analysis of dental implant, which the structural parameters have massive samples but the material of implant can only be selected from several Ti and its alloys. The prediction performance of the proposed approach is much better than the conventional SVR. The proposed approach can be used for the design, optimization and analysis of engineering systems with input parameters of unequal sample sizes.

Over the past few years the Angry Birds AI competition has been held in an attempt to develop intelligent agents that can successfully and efficiently solve levels for the video game Angry Birds. Many different agents and strategies have been developed to solve the complex and challenging physical reasoning problems associated with such a game. However none of these agents attempt one of the key strategies which humans employ to solve Angry Birds levels, which is restarting levels. Restarting is important in Angry Birds because sometimes the level is no longer solvable or some given shot made has little to no benefit towards the ultimate goal of the game. This paper proposes a framework and experimental evaluation for when to restart levels in Angry Birds. We demonstrate that restarting is a viable strategy to improve agent performance in many cases.

With the rapid growth of data, distributed stochastic gradient descent~(DSGD) has been widely used for solving large-scale machine learning problems. Due to the latency and limited bandwidth of network, communication has become the bottleneck of DSGD when we need to train large scale models, like deep neural networks. Communication compression with sparsified gradient, abbreviated as \emph{sparse communication}, has been widely used for reducing communication cost in DSGD. Recently, there has appeared one method, called deep gradient compression~(DGC), to combine memory gradient and momentum SGD for sparse communication. DGC has achieved promising performance in practise. However, the theory about the convergence of DGC is lack. In this paper, we propose a novel method, called \emph{\underline{g}}lobal \emph{\underline{m}}omentum \emph{\underline{c}}ompression~(GMC), for sparse communication in DSGD. GMC also combines memory gradient and momentum SGD. But different from DGC which adopts local momentum, GMC adopts global momentum. We theoretically prove the convergence rate of GMC for both convex and non-convex problems. To the best of our knowledge, this is the first work that proves the convergence of distributed momentum SGD~(DMSGD) with sparse communication and memory gradient. Empirical results show that, compared with the DMSGD counterpart without sparse communication, GMC can reduce the communication cost by approximately 100 fold without loss of generalization accuracy. GMC can also achieve comparable~(sometimes better) performance compared with DGC, with extra theoretical guarantee.

In this paper, we present a scalable distributed implementation of the sampled LSR1 (S-LSR1) algorithm. First, we show that a naive distributed implementation of S-LSR1 requires multiple rounds of expensive communications at every iteration and thus is inefficient. We then propose DS-LSR1, a communication-efficient variant of the S-LSR1 method, that drastically reduces the amount of data communicated at every iteration, that has favorable work-load balancing across nodes and that is matrix-free and inverse-free. The proposed method scales well in terms of both the dimension of the problem and the number of data points. Finally, we illustrate the performance of DS-LSR1 on standard neural network training tasks.

We address the problem of imitation learning with multi-modal demonstrations. Instead of attempting to learn all modes, we argue that in many tasks it is sufficient to imitate any one of them. We show that the state-of-the-art methods such as GAIL and behavior cloning, due to their choice of loss function, often incorrectly interpolate between such modes. Our key insight is to minimize the right divergence between the learner and the expert state-action distributions, namely the reverse KL divergence or I-projection. We propose a general imitation learning framework for estimating and minimizing any f-Divergence. By plugging in different divergences, we are able to recover existing algorithms such as Behavior Cloning (Kullback-Leibler), GAIL (Jensen Shannon) and DAGGER (Total Variation). Empirical results show that our approximate I-projection technique is able to imitate multi-modal behaviors more reliably than GAIL and behavior cloning.

The present study aims to investigate similarities between how humans and connectionist models experience difficulty in arithmetic problems. Problem difficulty was operationalized by the number of carries involved in solving a given problem. Problem difficulty was measured in humans by response time, and in models by computational steps. The present study found that both humans and connectionist models experience difficulty similarly when solving binary addition and subtraction. Specifically, both agents found difficulty to be strictly increasing with respect to the number of carries. Another notable similarity is that problem difficulty increases more steeply in subtraction than in addition, for both humans and connectionist models. Further investigation on two model hyperparameters --- confidence threshold and hidden dimension --- shows higher confidence thresholds cause the model to take more computational steps to arrive at the correct answer. Likewise, larger hidden dimensions cause the model to take more computational steps to correctly answer arithmetic problems; however, this effect by hidden dimensions is negligible.

While graph kernels (GKs) are easy to train and enjoy provable theoretical guarantees, their practical performances are limited by their expressive power, as the kernel function often depends on hand-crafted combinatorial features of graphs. Compared to graph kernels, graph neural networks (GNNs) usually achieve better practical performance, as GNNs use multi-layer architectures and non-linear activation functions to extract high-order information of graphs as features. However, due to the large number of hyper-parameters and the non-convex nature of the training procedure, GNNs are harder to train. Theoretical guarantees of GNNs are also not well-understood. Furthermore, the expressive power of GNNs scales with the number of parameters, and thus it is hard to exploit the full power of GNNs when computing resources are limited. The current paper presents a new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to \emph{infinitely wide} multi-layer GNNs trained by gradient descent. GNTKs enjoy the full expressive power of GNNs and inherit advantages of GKs. Theoretically, we show GNTKs provably learn a class of smooth functions on graphs. Empirically, we test GNTKs on graph classification datasets and show they achieve strong performance.

Attributed graphs, which contain rich contextual features beyond just network structure, are ubiquitous and have been observed to benefit various network analytics applications. Graph structure optimization, aiming to find the optimal graphs in terms of some specific measures, has become an effective computational tool in complex network analysis. However, traditional model-free methods suffer from the expensive computational cost of evaluating graphs; existing vectorial Bayesian optimization methods cannot be directly applied to attributed graphs and have the scalability issue due to the use of Gaussian processes (GPs). To bridge the gap, in this paper, we propose a novel scalable Deep Graph Bayesian Optimization (DGBO) method on attributed graphs. The proposed DGBO prevents the cubical complexity of the GPs by adopting a deep graph neural network to surrogate black-box functions, and can scale linearly with the number of observations. Intensive experiments are conducted on both artificial and real-world problems, including molecular discovery and urban road network design, and demonstrate the effectiveness of the DGBO compared with the state-of-the-art.

In this paper, we propose a novel structure for a cross-modal data association, which is inspired by the recent research on the associative learning structure of the brain. We formulate the cross-modal association in Bayesian inference framework realized by a deep neural network with multiple variational auto-encoders and variational associators. The variational associators transfer the latent spaces between auto-encoders that represent different modalities. The proposed structure successfully associates even heterogeneous modal data and easily incorporates the additional modality to the entire network via the proposed cross-modal associator. Furthermore, the proposed structure can be trained with only a small amount of paired data since auto-encoders can be trained by unsupervised manner. Through experiments, the effectiveness of the proposed structure is validated on various datasets including visual and auditory data.