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Register a new userWhen Is Generalizable Reinforcement Learning Tractable?
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Added by
Dhruv Malik
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Agents trained by reinforcement learning (RL) often fail to generalize beyond the environment they were trained in, even when presented with new scenarios that seem similar to the training environment. We study the query complexity required to train RL agents that generalize to multiple environments. Intuitively, tractable generalization is only possible when the environments are similar or close in some sense. To capture this, we introduce Weak Proximity, a natural structural condition that requires the environments to have highly similar transition and reward functions and share a policy providing optimal value. Despite such shared structure, we prove that tractable generalization is impossible in the worst case. This holds even when each individual environment can be efficiently solved to obtain an optimal linear policy, and when the agent possesses a generative model. Our lower bound applies to the more complex task of representation learning for the purpose of efficient generalization to multiple environments. On the positive side, we introduce Strong Proximity, a strengthened condition which we prove is sufficient for efficient generalization.
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We examine the question of when and how parametric models are most useful in reinforcement learning. In particular, we look at commonalities and differences between parametric models and experience replay. Replay-based learning algorithms share important traits with model-based approaches, including the ability to plan: to use more computation without additional data to improve predictions and behaviour. We discuss when to expect benefits from either approach, and interpret prior work in this context. We hypothesise that, under suitable conditions, replay-based algorithms should be competitive to or better than model-based algorithms if the model is used only to generate fictional transitions from observed states for an update rule that is otherwise model-free. We validated this hypothesis on Atari 2600 video games. The replay-based algorithm attained state-of-the-art data efficiency, improving over prior results with parametric models.
Episodic memory-based methods can rapidly latch onto past successful strategies by a non-parametric memory and improve sample efficiency of traditional reinforcement learning. However, little effort is put into the continuous domain, where a state is never visited twice, and previous episodic methods fail to efficiently aggregate experience across trajectories. To address this problem, we propose Generalizable Episodic Memory (GEM), which effectively organizes the state-action values of episodic memory in a generalizable manner and supports implicit planning on memorized trajectories. GEM utilizes a double estimator to reduce the overestimation bias induced by value propagation in the planning process. Empirical evaluation shows that our method significantly outperforms existing trajectory-based methods on various MuJoCo continuous control tasks. To further show the general applicability, we evaluate our method on Atari games with discrete action space, which also shows a significant improvement over baseline algorithms.
We consider the problem of learning an unknown ReLU network with respect to Gaussian inputs and obtain the first nontrivial results for networks of depth more than two. We give an algorithm whose running time is a fixed polynomial in the ambient dimension and some (exponentially large) function of only the networks parameters. Our bounds depend on the number of hidden units, depth, spectral norm of the weight matrices, and Lipschitz constant of the overall network (we show that some dependence on the Lipschitz constant is necessary). We also give a bound that is doubly exponential in the size of the network but is independent of spectral norm. These results provably cannot be obtained using gradient-based methods and give the first example of a class of efficiently learnable neural networks that gradient descent will fail to learn. In contrast, prior work for learning networks of depth three or higher requires exponential time in the ambient dimension, even when the above parameters are bounded by a constant. Additionally, all prior work for the depth-two case requires well-conditioned weights and/or positive coefficients to obtain efficient run-times. Our algorithm does not require these assumptions. Our main technical tool is a type of filtered PCA that can be used to iteratively recover an approximate basis for the subspace spanned by the hidden units in the first layer. Our analysis leverages new structural results on lattice polynomials from tropical geometry.
Much of the current work on reinforcement learning studies episodic settings, where the agent is reset between trials to an initial state distribution, often with well-shaped reward functions. Non-episodic settings, where the agent must learn through continuous interaction with the world without resets, and where the agent receives only delayed and sparse reward signals, is substantially more difficult, but arguably more realistic considering real-world environments do not present the learner with a convenient reset mechanism and easy reward shaping. In this paper, instead of studying algorithmic improvements that can address such non-episodic and sparse reward settings, we instead study the kinds of environment properties that can make learning under such conditions easier. Understanding how properties of the environment impact the performance of reinforcement learning agents can help us to structure our tasks in ways that make learning tractable. We first discuss what we term environment shaping -- modifications to the environment that provide an alternative to reward shaping, and may be easier to implement. We then discuss an even simpler property that we refer to as dynamism, which describes the degree to which the environment changes independent of the agents actions and can be measured by environment transition entropy. Surprisingly, we find that even this property can substantially alleviate the challenges associated with non-episodic RL in sparse reward settings. We provide an empirical evaluation on a set of new tasks focused on non-episodic learning with sparse rewards. Through this study, we hope to shift the focus of the community towards analyzing how properties of the environment can affect learning and the ultimate type of behavior that is learned via RL.
Given data drawn from an unknown distribution, $D$, to what extent is it possible to ``amplify this dataset and output an even larger set of samples that appear to have been drawn from $D$? We formalize this question as follows: an $(n,m)$ $text{amplification procedure}$ takes as input $n$ independent draws from an unknown distribution $D$, and outputs a set of $m > n$ ``samples. An amplification procedure is valid if no algorithm can distinguish the set of $m$ samples produced by the amplifier from a set of $m$ independent draws from $D$, with probability greater than $2/3$. Perhaps surprisingly, in many settings, a valid amplification procedure exists, even when the size of the input dataset, $n$, is significantly less than what would be necessary to learn $D$ to non-trivial accuracy. Specifically we consider two fundamental settings: the case where $D$ is an arbitrary discrete distribution supported on $le k$ elements, and the case where $D$ is a $d$-dimensional Gaussian with unknown mean, and fixed covariance. In the first case, we show that an $left(n, n + Theta(frac{n}{sqrt{k}})right)$ amplifier exists. In particular, given $n=O(sqrt{k})$ samples from $D$, one can output a set of $m=n+1$ datapoints, whose total variation distance from the distribution of $m$ i.i.d. draws from $D$ is a small constant, despite the fact that one would need quadratically more data, $n=Theta(k)$, to learn $D$ up to small constant total variation distance. In the Gaussian case, we show that an $left(n,n+Theta(frac{n}{sqrt{d}} )right)$ amplifier exists, even though learning the distribution to small constant total variation distance requires $Theta(d)$ samples. In both the discrete and Gaussian settings, we show that these results are tight, to constant factors. Beyond these results, we formalize a number of curious directions for future research along this vein.
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