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Humans tend to learn complex abstract concepts faster if examples are presented in a structured manner. For instance, when learning how to play a board game, usually one of the first concepts learned is how the game ends, i.e. the actions that lead to a terminal state (win, lose or draw). The advantage of learning end-games first is that once the actions which lead to a terminal state are understood, it becomes possible to incrementally learn the consequences of actions that are further away from a terminal state - we call this an end-game-first curriculum. Currently the state-of-the-art machine learning player for general board games, AlphaZero by Google DeepMind, does not employ a structured training curriculum; instead learning from the entire game at all times. By employing an end-game-first training curriculum to train an AlphaZero inspired player, we empirically show that the rate of learning of an artificial player can be improved during the early stages of training when compared to a player not using a training curriculum.
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Deep reinforcement learning (RL) has shown great empirical successes, but suffers from brittleness and sample inefficiency. A potential remedy is to use a previously-trained policy as a source of supervision. In this work, we refer to these policies as teachers and study how to transfer their expertise to new student policies by focusing on data usage. We propose a framework, Data CUrriculum for Reinforcement learning (DCUR), which first trains teachers using online deep RL, and stores the logged environment interaction history. Then, students learn by running either offline RL or by using teacher data in combination with a small amount of self-generated data. DCURs central idea involves defining a class of data curricula which, as a function of training time, limits the student to sampling from a fixed subset of the full teacher data. We test teachers and students using state-of-the-art deep RL algorithms across a variety of data curricula. Results suggest that the choice of data curricula significantly impacts student learning, and that it is beneficial to limit the data during early training stages while gradually letting the data availability grow over time. We identify when the student can learn offline and match teacher performance without relying on specialized offline RL algorithms. Furthermore, we show that collecting a small fraction of online data provides complementary benefits with the data curriculum. Supplementary material is available at https://tinyurl.com/teach-dcur.
Robust Reinforcement Learning aims to find the optimal policy with some extent of robustness to environmental dynamics. Existing learning algorithms usually enable the robustness through disturbing the current state or simulating environmental parameters in a heuristic way, which lack quantified robustness to the system dynamics (i.e. transition probability). To overcome this issue, we leverage Wasserstein distance to measure the disturbance to the reference transition kernel. With Wasserstein distance, we are able to connect transition kernel disturbance to the state disturbance, i.e. reduce an infinite-dimensional optimization problem to a finite-dimensional risk-aware problem. Through the derived risk-aware optimal Bellman equation, we show the existence of optimal robust policies, provide a sensitivity analysis for the perturbations, and then design a novel robust learning algorithm--Wasserstein Robust Advantage Actor-Critic algorithm (WRAAC). The effectiveness of the proposed algorithm is verified in the Cart-Pole environment.
Deep neural networks (DNNs) have great expressive power, which can even memorize samples with wrong labels. It is vitally important to reiterate robustness and generalization in DNNs against label corruption. To this end, this paper studies the 0-1 loss, which has a monotonic relationship with an empirical adversary (reweighted) risk~citep{hu2016does}. Although the 0-1 loss has some robust properties, it is difficult to optimize. To efficiently optimize the 0-1 loss while keeping its robust properties, we propose a very simple and efficient loss, i.e. curriculum loss (CL). Our CL is a tighter upper bound of the 0-1 loss compared with conventional summation based surrogate losses. Moreover, CL can adaptively select samples for model training. As a result, our loss can be deemed as a novel perspective of curriculum sample selection strategy, which bridges a connection between curriculum learning and robust learning. Experimental results on benchmark datasets validate the robustness of the proposed loss.
Despite many algorithmic advances, our theoretical understanding of practical distributional reinforcement learning methods remains limited. One exception is Rowland et al. (2018)s analysis of the C51 algorithm in terms of the Cramer distance, but their results only apply to the tabular setting and ignore C51s use of a softmax to produce normalized distributions. In this paper we adapt the Cramer distance to deal with arbitrary vectors. From it we derive a new distributional algorithm which is fully Cramer-based and can be combined to linear function approximation, with formal guarantees in the context of policy evaluation. In allowing the models prediction to be any real vector, we lose the probabilistic interpretation behind the method, but otherwise maintain the appealing properties of distributional approaches. To the best of our knowledge, ours is the first proof of convergence of a distributional algorithm combined with function approximation. Perhaps surprisingly, our results provide evidence that Cramer-based distributional methods may perform worse than directly approximating the value function.
We consider the problem of learning to behave optimally in a Markov Decision Process when a reward function is not specified, but instead we have access to a set of demonstrators of varying performance. We assume the demonstrators are classified into one of k ranks, and use ideas from ordinal regression to find a reward function that maximizes the margin between the different ranks. This approach is based on the idea that agents should not only learn how to behave from experts, but also how not to behave from non-experts. We show there are MDPs where important differences in the reward function would be hidden from existing algorithms by the behaviour of the expert. Our method is particularly useful for problems where we have access to a large set of agent behaviours with varying degrees of expertise (such as through GPS or cellphones). We highlight the differences between our approach and existing methods using a simple grid domain and demonstrate its efficacy on determining passenger-finding strategies for taxi drivers, using a large dataset of GPS trajectories.
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