Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite nonlinearity and non-convexity introduced by the implicit representation. Furthermore, we derive convergence rates for both cases which allow us to identify conditions under which stochastic gradient descent (SGD) with this implicit representation converges substantially faster than its explicit counterpart. Finally, we provide empirical results in some simple domains that illustrate the theoretical findings.

Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite nonlinearity and non-convexity introduced by the implicit representation. Furthermore, we derive convergence rates for both cases which allow us to identify conditions under which stochastic gradient descent (SGD) with this implicit representation converges substantially faster than its explicit counterpart. Finally, we provide empirical results in some simple domains that illustrate the theoretical findings.

While knowntobesample efficient, these methods havefailed tofully leverage recent advances indeep learning, forcing the use of less efficient but more scalable model-free methods which try to learn the values directly.

While knowntobesample efficient, these methods havefailed tofully leverage recent advances indeep learning, forcing the use of less efficient but more scalable model-free methods which try to learn the values directly.

Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite non-linearity and non-convexity introduced by the implicit representation. Furthermore, we derive convergence rates for both cases which allow us to identify conditions under which stochastic gradient descent (SGD) with this implicit representation converges substantially faster than its explicit counterpart. Finally, we provide empirical results in some simple domains that illustrate the theoretical findings.

Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite non-linearity and non-convexity introduced by the implicit representation.

Estimating the per-state expected cumulative rewards is a critical aspect of reinforcement learning approaches, however the experience is obtained, but standard deep neural-network function-approximation methods are often inefficient in this setting. An alternative approach, exemplified by value iteration networks, is to learn transition and reward models of a latent Markov decision process whose value predictions fit the data. This approach has been shown empirically to converge faster to a more robust solution in many cases, but there has been little theoretical study of this phenomenon. In this paper, we explore such implicit representations of value functions via theory and focused experimentation. We prove that, for a linear parametrization, gradient descent converges to global optima despite non-linearity and non-convexity introduced by the implicit representation.

We propose an unsupervised technique for implicit parameterization of data manifolds. In our approach, the data is assumed to belong to a lower dimensional manifold in a higher dimensional space, and the data points are viewed as the endpoints of the trajectories originating outside the manifold. Under this assumption, the data manifold is an attractive manifold of a dynamical system to be estimated. We parameterize such a dynamical system with a residual neural network and propose a spectral localization technique to ensure it is locally attractive in the vicinity of data. We also present initialization and additional regularization of the proposed residual layers. % that we call dissipative bottlenecks. We mention the importance of the considered problem for the tasks of reinforcement learning and support our discussion with examples demonstrating the performance of the proposed layers in denoising and generative tasks.