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A Bayesian treatment can mitigate overconfidence in ReLU nets around the training data. But far away from them, ReLU Bayesian neural networks (BNNs) can still underestimate uncertainty and thus be asymptotically overconfident. This issue arises since the output variance of a BNN with finitely many features is quadratic in the distance from the data region. Meanwhile, Bayesian linear models with ReLU features converge, in the infinite-width limit, to a particular Gaussian process (GP) with a variance that grows cubically so that no asymptotic overconfidence can occur. While this may seem of mostly theoretical interest, in this work, we show that it can be used in practice to the benefit of BNNs. We extend finite ReLU BNNs with infinite ReLU features via the GP and show that the resulting model is asymptotically maximally uncertain far away from the data while the BNNs' predictive power is unaffected near the data. Although the resulting model approximates a full GP posterior, thanks to its structure, it can be applied \emph{post-hoc} to any pre-trained ReLU BNN at a low cost.

Recently Reinforcement Learning (RL) has been applied as an anti-adversarial remedy in wireless communication networks. However, studying the RL-based approaches from the adversary's perspective has received little attention. Additionally, RL-based approaches in an anti-adversary or adversarial paradigm mostly consider single-channel communication (either channel selection or single channel power control), while multi-channel communication is more common in practice. In this paper, we propose a multi-agent adversary system (MAAS) for modeling and analyzing adversaries in a wireless communication scenario by careful design of the reward function under realistic communication scenarios. In particular, by modeling the adversaries as learning agents, we show that the proposed MAAS is able to successfully choose the transmitted channel(s) and their respective allocated power(s) without any prior knowledge of the sender strategy. Compared to the single-agent adversary (SAA), multi-agents in MAAS can achieve significant reduction in signal-to-noise ratio (SINR) under the same power constraints and partial observability, while providing improved stability and a more efficient learning process. Moreover, through empirical studies we show that the results in simulation are close to the ones in communication in reality, a conclusion that is pivotal to the validity of performance of agents evaluated in simulations.

Spurred in part by the ever-growing number of sensors and web-based methods of collecting data, the use of Intensive Longitudinal Data (ILD) is becoming more common in the social and behavioural sciences. The ILD collected in this field are often hypothesised to be the result of latent states (e.g. behaviour, emotions), and the promise of ILD lies in its ability to capture the dynamics of these states as they unfold in time. In particular, by collecting data for multiple subjects, researchers can observe how such dynamics differ between subjects. The Bayesian Multilevel Hidden Markov Model (mHMM) is a relatively novel model that is suited to model the ILD of this kind while taking into account heterogeneity between subjects. While the mHMM has been applied in a variety of settings, large-scale studies that examine the required sample size for this model are lacking. In this paper, we address this research gap by conducting a simulation study to evaluate the effect of changing (1) the number of subjects, (2) the number of occasions, and (3) the between subjects variability on parameter estimates obtained by the mHMM. We frame this simulation study in the context of sleep research, which consists of multivariate continuous data that displays considerable overlap in the state dependent component distributions. In addition, we generate a set of baseline scenarios with more general data properties. Overall, the number of subjects has the largest effect on model performance. However, the number of occasions is important to adequately model latent state transitions. We discuss how the characteristics of the data influence parameter estimation and provide recommendations to researchers seeking to apply the mHMM to their own data.

Deep-unfolding neural networks (NNs) have received great attention since they achieve satisfactory performance with relatively low complexity. Typically, these deep-unfolding NNs are restricted to a fixed-depth for all inputs. However, the optimal number of layers required for convergence changes with different inputs. In this paper, we first develop a framework of deep deterministic policy gradient (DDPG)-driven deep-unfolding with adaptive depth for different inputs, where the trainable parameters of deep-unfolding NN are learned by DDPG, rather than updated by the stochastic gradient descent algorithm directly. Specifically, the optimization variables, trainable parameters, and architecture of deep-unfolding NN are designed as the state, action, and state transition of DDPG, respectively. Then, this framework is employed to deal with the channel estimation problem in massive multiple-input multiple-output systems. Specifically, first of all we formulate the channel estimation problem with an off-grid basis and develop a sparse Bayesian learning (SBL)-based algorithm to solve it. Secondly, the SBL-based algorithm is unfolded into a layer-wise structure with a set of introduced trainable parameters. Thirdly, the proposed DDPG-driven deep-unfolding framework is employed to solve this channel estimation problem based on the unfolded structure of the SBL-based algorithm. To realize adaptive depth, we design the halting score to indicate when to stop, which is a function of the channel reconstruction error. Furthermore, the proposed framework is extended to realize the adaptive depth of the general deep neural networks (DNNs). Simulation results show that the proposed algorithm outperforms the conventional optimization algorithms and DNNs with fixed depth with much reduced number of layers.

Graph Neural Networks (GNNs) have been studied from the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

We study the problem of learning in the stochastic shortest path (SSP) setting, where an agent seeks to minimize the expected cost accumulated before reaching a goal state. We design a novel model-based algorithm EB-SSP that carefully skews the empirical transitions and perturbs the empirical costs with an exploration bonus to guarantee both optimism and convergence of the associated value iteration scheme. We prove that EB-SSP achieves the minimax regret rate $\widetilde{O}(B_{\star} \sqrt{S A K})$, where $K$ is the number of episodes, $S$ is the number of states, $A$ is the number of actions and $B_{\star}$ bounds the expected cumulative cost of the optimal policy from any state, thus closing the gap with the lower bound. Interestingly, EB-SSP obtains this result while being parameter-free, i.e., it does not require any prior knowledge of $B_{\star}$, nor of $T_{\star}$ which bounds the expected time-to-goal of the optimal policy from any state. Furthermore, we illustrate various cases (e.g., positive costs, or general costs when an order-accurate estimate of $T_{\star}$ is available) where the regret only contains a logarithmic dependence on $T_{\star}$, thus yielding the first horizon-free regret bound beyond the finite-horizon MDP setting.

Social relations are often used to improve recommendation quality when user-item interaction data is sparse in recommender systems. Most existing social recommendation models exploit pairwise relations to mine potential user preferences. However, real-life interactions among users are very complicated and user relations can be high-order. Hypergraph provides a natural way to model complex high-order relations, while its potentials for improving social recommendation are under-explored. In this paper, we fill this gap and propose a multi-channel hypergraph convolutional network to enhance social recommendation by leveraging high-order user relations. Technically, each channel in the network encodes a hypergraph that depicts a common high-order user relation pattern via hypergraph convolution. By aggregating the embeddings learned through multiple channels, we obtain comprehensive user representations to generate recommendation results. However, the aggregation operation might also obscure the inherent characteristics of different types of high-order connectivity information. To compensate for the aggregating loss, we innovatively integrate self-supervised learning into the training of the hypergraph convolutional network to regain the connectivity information with hierarchical mutual information maximization. The experimental results on multiple real-world datasets show that the proposed model outperforms the SOTA methods, and the ablation study verifies the effectiveness of the multi-channel setting and the self-supervised task. The implementation of our model is available via //github.com/Coder-Yu/RecQ.

Deep reinforcement learning (RL) has achieved many recent successes, yet experiment turn-around time remains a key bottleneck in research and in practice. We investigate how to optimize existing deep RL algorithms for modern computers, specifically for a combination of CPUs and GPUs. We confirm that both policy gradient and Q-value learning algorithms can be adapted to learn using many parallel simulator instances. We further find it possible to train using batch sizes considerably larger than are standard, without negatively affecting sample complexity or final performance. We leverage these facts to build a unified framework for parallelization that dramatically hastens experiments in both classes of algorithm. All neural network computations use GPUs, accelerating both data collection and training. Our results include using an entire DGX-1 to learn successful strategies in Atari games in mere minutes, using both synchronous and asynchronous algorithms.

Policy gradient methods are widely used in reinforcement learning algorithms to search for better policies in the parameterized policy space. They do gradient search in the policy space and are known to converge very slowly. Nesterov developed an accelerated gradient search algorithm for convex optimization problems. This has been recently extended for non-convex and also stochastic optimization. We use Nesterov's acceleration for policy gradient search in the well-known actor-critic algorithm and show the convergence using ODE method. We tested this algorithm on a scheduling problem. Here an incoming job is scheduled into one of the four queues based on the queue lengths. We see from experimental results that algorithm using Nesterov's acceleration has significantly better performance compared to algorithm which do not use acceleration. To the best of our knowledge this is the first time Nesterov's acceleration has been used with actor-critic algorithm.

In this paper, we study the optimal convergence rate for distributed convex optimization problems in networks. We model the communication restrictions imposed by the network as a set of affine constraints and provide optimal complexity bounds for four different setups, namely: the function $F(\xb) \triangleq \sum_{i=1}^{m}f_i(\xb)$ is strongly convex and smooth, either strongly convex or smooth or just convex. Our results show that Nesterov's accelerated gradient descent on the dual problem can be executed in a distributed manner and obtains the same optimal rates as in the centralized version of the problem (up to constant or logarithmic factors) with an additional cost related to the spectral gap of the interaction matrix. Finally, we discuss some extensions to the proposed setup such as proximal friendly functions, time-varying graphs, improvement of the condition numbers.