In this paper we show that restricting the representation-layer of a Recurrent Neural Network (RNN) improves accuracy and reduces the depth of recursive training procedures in partially observable domains. Artificial Neural Networks have been shown to learn useful state representations for high-dimensional visual and continuous control domains. If the the tasks at hand exhibits long depends back in time, these instantaneous feed-forward approaches are augmented with recurrent connections and trained with Back-prop Through Time (BPTT). This unrolled training can become computationally prohibitive if the dependency structure is long, and while recent work on LSTMs and GRUs has improved upon naive training strategies, there is still room for improvements in computational efficiency and parameter sensitivity. In this paper we explore a simple modification to the classic RNN structure: restricting the state to be comprised of multi-step General Value Function predictions. We formulate an architecture called General Value Function Networks (GVFNs), and corresponding objective that generalizes beyond previous approaches. We show that our GVFNs are significantly more robust to train, and facilitate accurate prediction with no gradients needed back-in-time in domains with substantial long-term dependences.
Recent work has shown that reinforcement learning (RL) is a promising approach to control dynamical systems described by partial differential equations (PDE). This paper shows how to use RL to tackle more general PDE control problems that have continuous high-dimensional action spaces with spatial relationship among action dimensions. In particular, we propose the concept of action descriptors, which encode regularities among spatially-extended action dimensions and enable the agent to control high-dimensional action PDEs. We provide theoretical evidence suggesting that this approach can be more sample efficient compared to a conventional approach that treats each action dimension separately and does not explicitly exploit the spatial regularity of the action space. The action descriptor approach is then used within the deep deterministic policy gradient algorithm. Experiments on two PDE control problems, with up to 256-dimensional continuous actions, show the advantage of the proposed approach over the conventional one.
Model-based strategies for control are critical to obtain sample efficient learning. Dyna is a planning paradigm that naturally interleaves learning and planning, by simulating one-step experience to update the action-value function. This elegant planning strategy has been mostly explored in the tabular setting. The aim of this paper is to revisit sample-based planning, in stochastic and continuous domains with learned models. We first highlight the flexibility afforded by a model over Experience Replay (ER). Replay-based methods can be seen as stochastic planning methods that repeatedly sample from a buffer of recent agent-environment interactions and perform updates to improve data efficiency. We show that a model, as opposed to a replay buffer, is particularly useful for specifying which states to sample from during planning, such as predecessor states that propagate information in reverse from a state more quickly. We introduce a semi-parametric model learning approach, called Reweighted Experience Models (REMs), that makes it simple to sample next states or predecessors. We demonstrate that REM-Dyna exhibits similar advantages over replay-based methods in learning in continuous state problems, and that the performance gap grows when moving to stochastic domains, of increasing size.
There is growing evidence that converting targets to soft targets in supervised learning can provide considerable gains in performance. Much of this work has considered classification, converting hard zero-one values to soft labels---such as by adding label noise, incorporating label ambiguity or using distillation. In parallel, there is some evidence from a regression setting in reinforcement learning that learning distributions can improve performance. In this work, we investigate the reasons for this improvement, in a regression setting. We introduce a novel distributional regression loss, and similarly find it significantly improves prediction accuracy. We investigate several common hypotheses, around reducing overfitting and improved representations. We instead find evidence for an alternative hypothesis: this loss is easier to optimize, with better behaved gradients, resulting in improved generalization. We provide theoretical support for this alternative hypothesis, by characterizing the norm of the gradients of this loss.
This paper investigates estimating the variance of a temporal-difference learning agent's update target. Most reinforcement learning methods use an estimate of the value function, which captures how good it is for the agent to be in a particular state and is mathematically expressed as the expected sum of discounted future rewards (called the return). These values can be straightforwardly estimated by averaging batches of returns using Monte Carlo methods. However, if we wish to update the agent's value estimates during learning--before terminal outcomes are observed--we must use a different estimation target called the {\lambda}-return, which truncates the return with the agent's own estimate of the value function. Temporal difference learning methods estimate the expected {\lambda}-return for each state, allowing these methods to update online and incrementally, and in most cases achieve better generalization error and faster learning than Monte Carlo methods. Naturally one could attempt to estimate higher-order moments of the {\lambda}-return. This paper is about estimating the variance of the {\lambda}-return. Prior work has shown that given estimates of the variance of the {\lambda}-return, learning systems can be constructed to (1) mitigate risk in action selection, and (2) automatically adapt the parameters of the learning process itself to improve performance. Unfortunately, existing methods for estimating the variance of the {\lambda}-return are complex and not well understood empirically. We contribute a method for estimating the variance of the {\lambda}-return directly using policy evaluation methods from reinforcement learning. Our approach is significantly simpler than prior methods that independently estimate the second moment of the {\lambda}-return. Empirically our new approach behaves at least as well as existing approaches, but is generally more robust.
Learning new representations of input observations in machine learning is often tackled using a factorization of the data. For many such problems, including sparse coding and matrix completion, learning these factorizations can be difficult, in terms of efficiency and to guarantee that the solution is a global minimum. Recently, a general class of objectives have been introduced-which we term induced dictionary learning models (DLMs)-that have an induced convex form that enables global optimization. Though attractive theoretically, this induced form is impractical, particularly for large or growing datasets. In this work, we investigate the use of practical alternating minimization algorithms for induced DLMs, that ensure convergence to global optima. We characterize the stationary points of these models, and, using these insights, highlight practical choices for the objectives. We then provide theoretical and empirical evidence that alternating minimization, from a random initialization, converges to global minima for a large subclass of induced DLMs. In particular, we take advantage of the existence of the (potentially unknown) convex induced form, to identify when stationary points are global minima for the dictionary learning objective. We then provide an empirical investigation into practical optimization choices for using alternating minimization for induced DLMs, for both batch and stochastic gradient descent.
High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive, particularly for matrix methods, such as least-squares temporal difference learning or quasi-Newton methods that approximate matrix step-sizes. In this work, we explore the utility of sketching for these two classes of algorithms. We highlight issues with sketching the high-dimensional features directly, which can incur significant bias. As a remedy, we demonstrate how to use sketching more sparingly, with only a left-sided sketch, that can still enable significant computational gains and the use of these matrix-based learning algorithms that are less sensitive to parameters. We empirically investigate these algorithms, in four domains with a variety of representations. Our aim is to provide insights into effective use of sketching in practice.
A variety of representation learning approaches have been investigated for reinforcement learning; much less attention, however, has been given to investigating the utility of sparse coding. Outside of reinforcement learning, sparse coding representations have been widely used, with non-convex objectives that result in discriminative representations. In this work, we develop a supervised sparse coding objective for policy evaluation. Despite the non-convexity of this objective, we prove that all local minima are global minima, making the approach amenable to simple optimization strategies. We empirically show that it is key to use a supervised objective, rather than the more straightforward unsupervised sparse coding approach. We compare the learned representations to a canonical fixed sparse representation, called tile-coding, demonstrating that the sparse coding representation outperforms a wide variety of tilecoding representations.
Reinforcement learning tasks are typically specified as Markov decision processes. This formalism has been highly successful, though specifications often couple the dynamics of the environment and the learning objective. This lack of modularity can complicate generalization of the task specification, as well as obfuscate connections between different task settings, such as episodic and continuing. In this work, we introduce the RL task formalism, that provides a unification through simple constructs including a generalization to transition-based discounting. Through a series of examples, we demonstrate the generality and utility of this formalism. Finally, we extend standard learning constructs, including Bellman operators, and extend some seminal theoretical results, including approximation errors bounds. Overall, we provide a well-understood and sound formalism on which to build theoretical results and simplify algorithm use and development.
The family of temporal difference (TD) methods span a spectrum from computationally frugal linear methods like TD({\lambda}) to data efficient least squares methods. Least square methods make the best use of available data directly computing the TD solution and thus do not require tuning a typically highly sensitive learning rate parameter, but require quadratic computation and storage. Recent algorithmic developments have yielded several sub-quadratic methods that use an approximation to the least squares TD solution, but incur bias. In this paper, we propose a new family of accelerated gradient TD (ATD) methods that (1) provide similar data efficiency benefits to least-squares methods, at a fraction of the computation and storage (2) significantly reduce parameter sensitivity compared to linear TD methods, and (3) are asymptotically unbiased. We illustrate these claims with a proof of convergence in expectation and experiments on several benchmark domains and a large-scale industrial energy allocation domain.