Within the context of trajectory planning for autonomous vehicles this paper proposes methods for efficient encoding of motion primitives in neural networks on top of model-based and gradient-free reinforcement learning. It is distinguished between 5 core aspects: system model, network architecture, training algorithm, training tasks selection and hardware software implementation. For the system model, a kinematic (3-states-2-controls) and a dynamic (16-states-2-controls) vehicle model are compared. For the network architecture, 3 feedforward structures are compared including weighted skip connections. For the training algorithm, virtual velocity constraints and network scheduling are proposed. For the training tasks, different feature vector selections are discussed. For the implementation, aspects of gradient-free learning using 1 GPU and the handling of perturbation noise therefore are discussed. The effects of proposed methods are illustrated in experiments encoding up to 14625 motion primitives. The capabilities of tiny neural networks with as few as 10 scalar parameters when scheduled on vehicle velocity are emphasized.
Regarding the training method, this paper is based on the TSHC-algorithm (task separation with hill climbing) @cite_24 , which itself was motivated by the ES-algorithm (evolution strategies) @cite_6 . Note that ES can be considered a gradient-based algorithm since it performs stochastic gradient descent via an operation similar to a finite-difference approximation of the gradient @cite_0 , however, generating more robust policies @cite_8 . In contrast, TSHC is a truely gradient-free algorithm (hill climbing), which is designed specifically for deterministic encoding of motion primitives in NNs. This paper differs from @cite_24 according to above listed 6 contributions.
@cite_24 @cite_0 @cite_6 @cite_8
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We present a new algorithm for Bayesian network structure learning, called Max-Min Hill-Climbing (MMHC). The algorithm combines ideas from local learning, constraint-based, and search-and-score techniques in a principled and effective way. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. In our extensive empirical evaluation MMHC outperforms on average and in terms of various metrics several prototypical and state-of-the-art algorithms, namely the PC, Sparse Candidate, Three Phase Dependency Analysis, Optimal Reinsertion, Greedy Equivalence Search, and Greedy Search. These are the first empirical results simultaneously comparing most of the major Bayesian network algorithms against each other. MMHC offers certain theoretical advantages, specifically over the Sparse Candidate algorithm, corroborated by our experiments. MMHC and detailed results of our study are publicly available at http: www.dsl-lab.org supplements mmhc_paper mmhc_index.html. We formulate gradient-based Markov chain Monte Carlo (MCMC) sampling as optimization on the space of probability measures, with Kullback-Leibler (KL) divergence as the objective function. We show that an underdamped form of the Langevin algorithm perform accelerated gradient descent in this metric. To characterize the convergence of the algorithm, we construct a Lyapunov functional and exploit hypocoercivity of the underdamped Langevin algorithm. As an application, we show that accelerated rates can be obtained for a class of nonconvex functions with the Langevin algorithm. Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC might suffer from poor mixing rates when random variables exhibit strong couplings under the target densities or big scale differences. In this study, we propose a novel SG-MCMC method that takes the local geometry into account by using ideas from Quasi-Newton optimization methods. These second order methods directly approximate the inverse Hessian by using a limited history of samples and their gradients. Our method uses dense approximations of the inverse Hessian while keeping the time and memory complexities linear with the dimension of the problem. We provide a formal theoretical analysis where we show that the proposed method is asymptotically unbiased and consistent with the posterior expectations. We illustrate the effectiveness of the approach on both synthetic and real datasets. Our experiments on two challenging applications show that our method achieves fast convergence rates similar to Riemannian approaches while at the same time having low computational requirements similar to diagonal preconditioning approaches. Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an SGMCMC algorithm. Furthermore, we extend recent SG-MCMC methods with two key components: i) adaptive preconditioners (as in ADAgrad or RMSprop), and ii) adaptive element-wise momentum weights. The zerotemperature limit gives a novel stochastic optimization method with adaptive elementwise momentum weights, while conventional optimization methods only have a shared, static momentum weight. Under certain assumptions, our theoretical analysis suggests the proposed simulated annealing approach converges close to the global optima. Experiments on several deep neural network models show state-of-the-art results compared to related stochastic optimization algorithms.