Kenny Young

Kenny Young, Aditya Ramesh, Louis Kirsch et al.

Model-Based Reinforcement Learning (RL) is widely believed to have the potential to improve sample efficiency by allowing an agent to synthesize large amounts of imagined experience. Experience Replay (ER) can be considered a simple kind of model, which has proved effective at improving the stability and efficiency of deep RL. In principle, a learned parametric model could improve on ER by generalizing from real experience to augment the dataset with additional plausible experience. However, given that learned value functions can also generalize, it is not immediately obvious why model generalization should be better. Here, we provide theoretical and empirical insight into when, and how, we can expect data generated by a learned model to be useful. First, we provide a simple theorem motivating how learning a model as an intermediate step can narrow down the set of possible value functions more than learning a value function directly from data using the Bellman equation. Second, we provide an illustrative example showing empirically how a similar effect occurs in a more concrete setting with neural network function approximation. Finally, we provide extensive experiments showing the benefit of model-based learning for online RL in environments with combinatorial complexity, but factored structure that allows a learned model to generalize. In these experiments, we take care to control for other factors in order to isolate, insofar as possible, the benefit of using experience generated by a learned model relative to ER alone.

Tian Tian, Kenny Young, Richard S. Sutton

Value iteration (VI) is a foundational dynamic programming method, important for learning and planning in optimal control and reinforcement learning. VI proceeds in batches, where the update to the value of each state must be completed before the next batch of updates can begin. Completing a single batch is prohibitively expensive if the state space is large, rendering VI impractical for many applications. Asynchronous VI helps to address the large state space problem by updating one state at a time, in-place and in an arbitrary order. However, Asynchronous VI still requires a maximization over the entire action space, making it impractical for domains with large action space. To address this issue, we propose doubly-asynchronous value iteration (DAVI), a new algorithm that generalizes the idea of asynchrony from states to states and actions. More concretely, DAVI maximizes over a sampled subset of actions that can be of any user-defined size. This simple approach of using sampling to reduce computation maintains similarly appealing theoretical properties to VI without the need to wait for a full sweep through the entire action space in each update. In this paper, we show DAVI converges to the optimal value function with probability one, converges at a near-geometric rate with probability 1-delta, and returns a near-optimal policy in computation time that nearly matches a previously established bound for VI. We also empirically demonstrate DAVI's effectiveness in several experiments.

Kenny Young, Richard S. Sutton

Discovering useful temporal abstractions, in the form of options, is widely thought to be key to applying reinforcement learning and planning to increasingly complex domains. Building on the empirical success of the Expert Iteration approach to policy learning used in AlphaZero, we propose Option Iteration, an analogous approach to option discovery. Rather than learning a single strong policy that is trained to match the search results everywhere, Option Iteration learns a set of option policies trained such that for each state encountered, at least one policy in the set matches the search results for some horizon into the future. Intuitively, this may be significantly easier as it allows the algorithm to hedge its bets compared to learning a single globally strong policy, which may have complex dependencies on the details of the current state. Having learned such a set of locally strong policies, we can use them to guide the search algorithm resulting in a virtuous cycle where better options lead to better search results which allows for training of better options. We demonstrate experimentally that planning using options learned with Option Iteration leads to a significant benefit in challenging planning environments compared to an analogous planning algorithm operating in the space of primitive actions and learning a single rollout policy with Expert Iteration.

Aditya A. Ramesh, Kenny Young, Louis Kirsch et al.

Temporal credit assignment in reinforcement learning is challenging due to delayed and stochastic outcomes. Monte Carlo targets can bridge long delays between action and consequence but lead to high-variance targets due to stochasticity. Temporal difference (TD) learning uses bootstrapping to overcome variance but introduces a bias that can only be corrected through many iterations. TD($λ$) provides a mechanism to navigate this bias-variance tradeoff smoothly. Appropriately selecting $λ$ can significantly improve performance. Here, we propose Chunked-TD, which uses predicted probabilities of transitions from a model for computing $λ$-return targets. Unlike other model-based solutions to credit assignment, Chunked-TD is less vulnerable to model inaccuracies. Our approach is motivated by the principle of history compression and 'chunks' trajectories for conventional TD learning. Chunking with learned world models compresses near-deterministic regions of the environment-policy interaction to speed up credit assignment while still bootstrapping when necessary. We propose algorithms that can be implemented online and show that they solve some problems much faster than conventional TD($λ$).

Kenny Young

Training neural networks with discrete stochastic variables presents a unique challenge. Backpropagation is not directly applicable, nor are the reparameterization tricks used in networks with continuous stochastic variables. To address this challenge, we present Hindsight Network Credit Assignment (HNCA), a novel gradient estimation algorithm for networks of discrete stochastic units. HNCA works by assigning credit to each unit based on the degree to which its output influences its immediate children in the network. We prove that HNCA produces unbiased gradient estimates with reduced variance compared to the REINFORCE estimator, while the computational cost is similar to that of backpropagation. We first apply HNCA in a contextual bandit setting to optimize a reward function that is unknown to the agent. In this setting, we empirically demonstrate that HNCA significantly outperforms REINFORCE, indicating that the variance reduction implied by our theoretical analysis is significant and impactful. We then show how HNCA can be extended to optimize a more general function of the outputs of a network of stochastic units, where the function is known to the agent. We apply this extended version of HNCA to train a discrete variational auto-encoder and empirically show it compares favourably to other strong methods. We believe that the ideas underlying HNCA can help stimulate new ways of thinking about efficient credit assignment in stochastic compute graphs.

Kenny Young

We present Hindsight Network Credit Assignment (HNCA), a novel learning method for stochastic neural networks, which works by assigning credit to each neuron's stochastic output based on how it influences the output of its immediate children in the network. We prove that HNCA provides unbiased gradient estimates while reducing variance compared to the REINFORCE estimator. We also experimentally demonstrate the advantage of HNCA over REINFORCE in a contextual bandit version of MNIST. The computational complexity of HNCA is similar to that of backpropagation. We believe that HNCA can help stimulate new ways of thinking about credit assignment in stochastic compute graphs.

Kenny Young, Richard S. Sutton

Despite empirical success, the theory of reinforcement learning (RL) with value function approximation remains fundamentally incomplete. Prior work has identified a variety of pathological behaviours that arise in RL algorithms that combine approximate on-policy evaluation and greedification. One prominent example is policy oscillation, wherein an algorithm may cycle indefinitely between policies, rather than converging to a fixed point. What is not well understood however is the quality of the policies in the region of oscillation. In this paper we present simple examples illustrating that in addition to policy oscillation and multiple fixed points -- the same basic issue can lead to convergence to the worst possible policy for a given approximation. Such behaviours can arise when algorithms optimize evaluation accuracy weighted by the distribution of states that occur under the current policy, but greedify based on the value of states which are rare or nonexistent under this distribution. This means the values used for greedification are unreliable and can steer the policy in undesirable directions. Our observation that this can lead to the worst possible policy shows that in a general sense such algorithms are unreliable. The existence of such examples helps to narrow the kind of theoretical guarantees that are possible and the kind of algorithmic ideas that are likely to be helpful. We demonstrate analytically and experimentally that such pathological behaviours can impact a wide range of RL and dynamic programming algorithms; such behaviours can arise both with and without bootstrapping, and with linear function approximation as well as with more complex parameterized functions like neural networks.

Kenny Young

Hindsight Credit Assignment (HCA) refers to a recently proposed family of methods for producing more efficient credit assignment in reinforcement learning. These methods work by explicitly estimating the probability that certain actions were taken in the past given present information. Prior work has studied the properties of such methods and demonstrated their behaviour empirically. We extend this work by introducing a particular HCA algorithm which has provably lower variance than the conventional Monte-Carlo estimator when the necessary functions can be estimated exactly. This result provides a strong theoretical basis for how HCA could be broadly useful.

Kenny Young, Tian Tian

The Arcade Learning Environment (ALE) is a popular platform for evaluating reinforcement learning agents. Much of the appeal comes from the fact that Atari games demonstrate aspects of competency we expect from an intelligent agent and are not biased toward any particular solution approach. The challenge of the ALE includes (1) the representation learning problem of extracting pertinent information from raw pixels, and (2) the behavioural learning problem of leveraging complex, delayed associations between actions and rewards. Often, the research questions we are interested in pertain more to the latter, but the representation learning problem adds significant computational expense. We introduce MinAtar, short for miniature Atari, a new set of environments that capture the general mechanics of specific Atari games while simplifying the representational complexity to focus more on the behavioural challenges. MinAtar consists of analogues of five Atari games: Seaquest, Breakout, Asterix, Freeway and Space Invaders. Each MinAtar environment provides the agent with a 10x10xn binary state representation. Each game plays out on a 10x10 grid with n channels corresponding to game-specific objects, such as ball, paddle and brick in the game Breakout. To investigate the behavioural challenges posed by MinAtar, we evaluated a smaller version of the DQN architecture as well as online actor-critic with eligibility traces. With the representation learning problem simplified, we can perform experiments with significantly less computational expense. In our experiments, we use the saved compute time to perform step-size parameter sweeps and more runs than is typical for the ALE. Experiments like this improve reproducibility, and allow us to draw more confident conclusions. We hope that MinAtar can allow researchers to thoroughly investigate behavioural challenges similar to those inherent in the ALE.

Kenny Young, Baoxiang Wang, Matthew E. Taylor

Reinforcement learning (RL) has had many successes in both "deep" and "shallow" settings. In both cases, significant hyperparameter tuning is often required to achieve good performance. Furthermore, when nonlinear function approximation is used, non-stationarity in the state representation can lead to learning instability. A variety of techniques exist to combat this --- most notably large experience replay buffers or the use of multiple parallel actors. These techniques come at the cost of moving away from the online RL problem as it is traditionally formulated (i.e., a single agent learning online without maintaining a large database of training examples). Meta-learning can potentially help with both these issues by tuning hyperparameters online and allowing the algorithm to more robustly adjust to non-stationarity in a problem. This paper applies meta-gradient descent to derive a set of step-size tuning algorithms specifically for online RL control with eligibility traces. Our novel technique, Metatrace, makes use of an eligibility trace analogous to methods like $TD(λ)$. We explore tuning both a single scalar step-size and a separate step-size for each learned parameter. We evaluate Metatrace first for control with linear function approximation in the classic mountain car problem and then in a noisy, non-stationary version. Finally, we apply Metatrace for control with nonlinear function approximation in 5 games in the Arcade Learning Environment where we explore how it impacts learning speed and robustness to initial step-size choice. Results show that the meta-step-size parameter of Metatrace is easy to set, Metatrace can speed learning, and Metatrace can allow an RL algorithm to deal with non-stationarity in the learning task.

Craig Sherstan, Brendan Bennett, Kenny Young et al.

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 λ-return, which truncates the return with the agent's own estimate of the value function. Temporal difference learning methods estimate the expected λ-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 λ-return. This paper is about estimating the variance of the λ-return. Prior work has shown that given estimates of the variance of the λ-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 λ-return are complex and not well understood empirically. We contribute a method for estimating the variance of the λ-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 λ-return. Empirically our new approach behaves at least as well as existing approaches, but is generally more robust.

Kenny Young, Ryan B. Hayward

We present Solrex,an automated solver for the game of Reverse Hex.Reverse Hex, also known as Rex, or Misere Hex, is the variant of the game of Hex in which the player who joins her two sides loses the game. Solrex performs a mini-max search of the state space using Scalable Parallel Depth First Proof Number Search, enhanced by the pruning of inferior moves and the early detection of certain winning strategies. Solrex is implemented on the same code base as the Hex program Solver, and can solve arbitrary positions on board sizes up to 6x6, with the hardest position taking less than four hours on four threads.

Kenny Young, Ryan Hayward, Gautham Vasan

DeepMind's recent spectacular success in using deep convolutional neural nets and machine learning to build superhuman level agents --- e.g. for Atari games via deep Q-learning and for the game of Go via Reinforcement Learning --- raises many questions, including to what extent these methods will succeed in other domains. In this paper we consider DQL for the game of Hex: after supervised initialization, we use selfplay to train NeuroHex, an 11-layer CNN that plays Hex on the 13x13 board. Hex is the classic two-player alternate-turn stone placement game played on a rhombus of hexagonal cells in which the winner is whomever connects their two opposing sides. Despite the large action and state space, our system trains a Q-network capable of strong play with no search. After two weeks of Q-learning, NeuroHex achieves win-rates of 20.4% as first player and 2.1% as second player against a 1-second/move version of MoHex, the current ICGA Olympiad Hex champion. Our data suggests further improvement might be possible with more training time.