Optimal policy evaluation using kernel-based temporal difference methods

We study methods based on reproducing kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process (MRP). We study a regularized form of the kernel least-squares temporal difference (LSTD) estimate; in the population limit of infinite data, it corresponds to the fixed point of a projected Bellman operator defined by the associated reproducing kernel Hilbert space. The estimator itself is obtained by computing the projected fixed point induced by a regularized version of the empirical operator; due to the underlying kernel structure, this reduces to solving a linear system involving kernel matrices. We analyze the error of this estimate in the $L^2(\mu)$-norm, where $\mu$ denotes the stationary distribution of the underlying Markov chain. Our analysis imposes no assumptions on the transition operator of the Markov chain, but rather only conditions on the reward function and population-level kernel LSTD solutions. We use empirical process theory techniques to derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator, as well as the instance-dependent variance of the Bellman residual error. In addition, we prove minimax lower bounds over sub-classes of MRPs, which shows that our rate is optimal in terms of the sample size $n$ and the effective horizon $H = (1 - \gamma)^{-1}$. Whereas existing worst-case theory predicts cubic scaling ($H^3$) in the effective horizon, our theory reveals that there is in fact a much wider range of scalings, depending on the kernel, the stationary distribution, and the variance of the Bellman residual error. Notably, it is only parametric and near-parametric problems that can ever achieve the worst-case cubic scaling.

Boosting the Convergence of Reinforcement Learning-based Auto-pruning Using Historical Data

Recently, neural network compression schemes like channel pruning have been widely used to reduce the model size and computational complexity of deep neural network (DNN) for applications in power-constrained scenarios such as embedded systems. Reinforcement learning (RL)-based auto-pruning has been further proposed to automate the DNN pruning process to avoid expensive hand-crafted work. However, the RL-based pruner involves a time-consuming training process and the high expense of each sample further exacerbates this problem. These impediments have greatly restricted the real-world application of RL-based auto-pruning. Thus, in this paper, we propose an efficient auto-pruning framework which solves this problem by taking advantage of the historical data from the previous auto-pruning process. In our framework, we first boost the convergence of the RL-pruner by transfer learning. Then, an augmented transfer learning scheme is proposed to further speed up the training process by improving the transferability. Finally, an assistant learning process is proposed to improve the sample efficiency of the RL agent. The experiments have shown that our framework can accelerate the auto-pruning process by 1.5-2.5 times for ResNet20, and 1.81-2.375 times for other neural networks like ResNet56, ResNet18, and MobileNet v1.

On the Sample Complexity and Metastability of Heavy-tailed Policy Search in Continuous Control

Reinforcement learning is a framework for interactive decision-making with incentives sequentially revealed across time without a system dynamics model. Due to its scaling to continuous spaces, we focus on policy search where one iteratively improves a parameterized policy with stochastic policy gradient (PG) updates. In tabular Markov Decision Problems (MDPs), under persistent exploration and suitable parameterization, global optimality may be obtained. By contrast, in continuous space, the non-convexity poses a pathological challenge as evidenced by existing convergence results being mostly limited to stationarity or arbitrary local extrema. To close this gap, we step towards persistent exploration in continuous space through policy parameterizations defined by distributions of heavier tails defined by tail-index parameter alpha, which increases the likelihood of jumping in state space. Doing so invalidates smoothness conditions of the score function common to PG. Thus, we establish how the convergence rate to stationarity depends on the policy's tail index alpha, a Holder continuity parameter, integrability conditions, and an exploration tolerance parameter introduced here for the first time. Further, we characterize the dependence of the set of local maxima on the tail index through an exit and transition time analysis of a suitably defined Markov chain, identifying that policies associated with Levy Processes of a heavier tail converge to wider peaks. This phenomenon yields improved stability to perturbations in supervised learning, which we corroborate also manifests in improved performance of policy search, especially when myopic and farsighted incentives are misaligned.

1$\times$N Block Pattern for Network Sparsity

Though network sparsity emerges as a promising direction to overcome the drastically increasing size of neural networks, it remains an open problem to concurrently maintain model accuracy as well as achieve significant speedups on general CPUs. In this paper, we propose one novel concept of $1\times N$ block sparsity pattern (block pruning) to break this limitation. In particular, consecutive $N$ output kernels with the same input channel index are grouped into one block, which serves as a basic pruning granularity of our pruning pattern. Our $1 \times N$ sparsity pattern prunes these blocks considered unimportant. We also provide a workflow of filter rearrangement that first rearranges the weight matrix in the output channel dimension to derive more influential blocks for accuracy improvements, and then applies similar rearrangement to the next-layer weights in the input channel dimension to ensure correct convolutional operations. Moreover, the output computation after our $1 \times N$ block sparsity can be realized via a parallelized block-wise vectorized operation, leading to significant speedups on general CPUs-based platforms. The efficacy of our pruning pattern is proved with experiments on ILSVRC-2012. For example, in the case of 50% sparsity and $N=4$, our pattern obtains about 3.0% improvements over filter pruning in the top-1 accuracy of MobileNet-V2. Meanwhile, it obtains 56.04ms inference savings on Cortex-A7 CPU over weight pruning. Code is available at https://github.com/lmbxmu/1xN.

You Only Compress Once: Towards Effective and Elastic BERT Compression via Exploit-Explore Stochastic Nature Gradient

Despite superior performance on various natural language processing tasks, pre-trained models such as BERT are challenged by deploying on resource-constraint devices. Most existing model compression approaches require re-compression or fine-tuning across diverse constraints to accommodate various hardware deployments. This practically limits the further application of model compression. Moreover, the ineffective training and searching process of existing elastic compression paradigms[4,27] prevents the direct migration to BERT compression. Motivated by the necessity of efficient inference across various constraints on BERT, we propose a novel approach, YOCO-BERT, to achieve compress once and deploy everywhere. Specifically, we first construct a huge search space with 10^13 architectures, which covers nearly all configurations in BERT model. Then, we propose a novel stochastic nature gradient optimization method to guide the generation of optimal candidate architecture which could keep a balanced trade-off between explorations and exploitation. When a certain resource constraint is given, a lightweight distribution optimization approach is utilized to obtain the optimal network for target deployment without fine-tuning. Compared with state-of-the-art algorithms, YOCO-BERT provides more compact models, yet achieving 2.1%-4.5% average accuracy improvement on the GLUE benchmark. Besides, YOCO-BERT is also more effective, e.g.,the training complexity is O(1)for N different devices. Code is availablehttps://github.com/MAC-AutoML/YOCO-BERT.

MARL with General Utilities via Decentralized Shadow Reward Actor-Critic

We posit a new mechanism for cooperation in multi-agent reinforcement learning (MARL) based upon any nonlinear function of the team's long-term state-action occupancy measure, i.e., a \emph{general utility}. This subsumes the cumulative return but also allows one to incorporate risk-sensitivity, exploration, and priors. % We derive the {\bf D}ecentralized {\bf S}hadow Reward {\bf A}ctor-{\bf C}ritic (DSAC) in which agents alternate between policy evaluation (critic), weighted averaging with neighbors (information mixing), and local gradient updates for their policy parameters (actor). DSAC augments the classic critic step by requiring agents to (i) estimate their local occupancy measure in order to (ii) estimate the derivative of the local utility with respect to their occupancy measure, i.e., the "shadow reward". DSAC converges to $\epsilon$-stationarity in $\mathcal{O}(1/\epsilon^{2.5})$ (Theorem \ref{theorem:final}) or faster $\mathcal{O}(1/\epsilon^{2})$ (Corollary \ref{corollary:communication}) steps with high probability, depending on the amount of communications. We further establish the non-existence of spurious stationary points for this problem, that is, DSAC finds the globally optimal policy (Corollary \ref{corollary:global}). Experiments demonstrate the merits of goals beyond the cumulative return in cooperative MARL.

Towards Compact CNNs via Collaborative Compression

Channel pruning and tensor decomposition have received extensive attention in convolutional neural network compression. However, these two techniques are traditionally deployed in an isolated manner, leading to significant accuracy drop when pursuing high compression rates. In this paper, we propose a Collaborative Compression (CC) scheme, which joints channel pruning and tensor decomposition to compress CNN models by simultaneously learning the model sparsity and low-rankness. Specifically, we first investigate the compression sensitivity of each layer in the network, and then propose a Global Compression Rate Optimization that transforms the decision problem of compression rate into an optimization problem. After that, we propose multi-step heuristic compression to remove redundant compression units step-by-step, which fully considers the effect of the remaining compression space (i.e., unremoved compression units). Our method demonstrates superior performance gains over previous ones on various datasets and backbone architectures. For example, we achieve 52.9% FLOPs reduction by removing 48.4% parameters on ResNet-50 with only a Top-1 accuracy drop of 0.56% on ImageNet 2012.

Learning Good State and Action Representations via Tensor Decomposition

The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning method to identify meaningful low-dimensional state and action representations from empirical trajectories. The method exploits the MDP's tensor structure by kernelization, importance sampling and low-Tucker-rank approximation. This method can be further used to cluster states and actions respectively and find the best discrete MDP abstraction. We provide sharp statistical error bounds for tensor concentration and the preservation of diffusion distance after embedding.

On the Convergence and Sample Efficiency of Variance-Reduced Policy Gradient Method

Policy gradient gives rise to a rich class of reinforcement learning (RL) methods, for example the REINFORCE. Yet the best known sample complexity result for such methods to find an $\epsilon$-optimal policy is $\mathcal{O}(\epsilon^{-3})$, which is suboptimal. In this paper, we study the fundamental convergence properties and sample efficiency of first-order policy optimization method. We focus on a generalized variant of policy gradient method, which is able to maximize not only a cumulative sum of rewards but also a general utility function over a policy's long-term visiting distribution. By exploiting the problem's hidden convex nature and leveraging techniques from composition optimization, we propose a Stochastic Incremental Variance-Reduced Policy Gradient (SIVR-PG) approach that improves a sequence of policies to provably converge to the global optimal solution and finds an $\epsilon$-optimal policy using $\tilde{\mathcal{O}}(\epsilon^{-2})$ samples.