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Title: Online Meta-Critic Learning for Off-Policy Actor-Critic Methods

Paper content:
Off-Policy Actor-Critic (Off-PAC) methods have proven successful in a variety of continuous control tasks.
Normally, the critic’s action-value function is updated using temporal-difference, and the critic in turn provides a loss for the actor that trains it to take actions with higher expected return.
In this paper, we introduce a novel and flexible meta-critic that observes the learning process and meta-learns an additional loss for the actor that accelerates and improves actor-critic learning.
Compared to the vanilla critic, the meta-critic network is explicitly trained to accelerate the learning process; and compared to existing meta-learning algorithms, meta-critic is rapidly learned online for a single task, rather than slowly over a family of tasks.
Crucially, our meta-critic framework is designed for off-policy based learners, which currently provide state-of-the-art reinforcement learning sample efficiency.
We demonstrate that online meta-critic learning leads to improvements in a variety of continuous control environments when combined with contemporary Off-PAC methods DDPG, TD3 and the state-of-the-art SAC.
Off-policy Actor-Critic (Off-PAC) methods are currently central in deep reinforcement learning (RL) research due to their greater sample efficiency compared to on-policy alternatives.
On-policy requires new trajectories to be collected for each update to the policy, and is expensive as the number of gradient steps and samples per step increases with task-complexity even for contemporary TRPO (Schulman et al., 2015) , PPO (Schulman et al., 2017) and A3C (Mnih et al., 2016) algorithms.
Off-policy methods, such as DDPG (Lillicrap et al., 2016) , TD3 (Fujimoto et al., 2018) and SAC (Haarnoja et al., 2018b) achieve greater sample efficiency due to their ability to learn from randomly sampled historical transitions without a time sequence requirement, thus making better use of past experience.
Their critic estimates the action-value (Q-value) function using a differentiable function approximator, and the actor updates its policy parameters in the direction of the approximate action-value gradient.
Briefly, the critic provides a loss to guide the actor, and is trained in turn to estimate the environmental action-value under the current policy via temporal-difference learning (Sutton et al., 2009) .
In all these cases the learning algorithm itself is hand-crafted and fixed.
Recently meta-learning, or "learning-to-learn" has become topical as a paradigm to accelerate RL by learning aspects of the learning strategy, for example, through learning fast adaptation strategies (Finn et al., 2017; Rakelly et al., 2019; Riemer et al., 2019) , exploration strategies (Gupta et al., 2018) , optimization strategies (Duan et al., 2016b) , losses (Houthooft et al., 2018) , hyperparameters (Xu et al., 2018; Veeriah et al., 2019) , and intrinsic rewards (Zheng et al., 2018) .
However, the majority of these works perform meta-learning on a family of tasks or environments and amortize this huge cost by deploying the trained strategy for fast learning on a new task.
In this paper we introduce a novel meta-critic network to enhance existing Off-PAC learning frameworks.
The meta-critic is used alongside the vanilla critic to provide a loss to guide the actor's learning.
However compared to the vanilla critic, the meta-critic is explicitly (meta)-trained to accelerate the learning process rather than merely estimate the action-value function.
Overall, the actor is trained by gradients provided by both critic and meta-critic losses, the critic is trained by temporal-difference as usual, and the meta-critic is trained to generate maximum learning performance improvements in the actor.
In our framework, both the critic and meta-critic use randomly sampled off-policy transitions for efficient and effective Off-PAC learning, providing superior sam-ple efficiency compared to existing on-policy meta-learners.
Furthermore, we demonstrate that our meta-critic can be successfully learned online within a single task.
This is in contrast to the currently widely used meta-learning research paradigm -where entire task families are required to provide enough data for meta-learning, and to provide new tasks to amortize the huge cost of meta-learning.
Essentially our framework meta-learns an auxiliary loss function, which can be seen as an intrinsic motivation towards optimum learning progress (Oudeyer & Kaplan, 2009) .
As analogously observed in several recent meta-learning studies (Franceschi et al., 2018) , our loss-learning can be formalized as a bi-level optimization problem with the upper level being meta-critic learning, and lower level being conventional learning.
We solve this joint optimization by iteratively updating the metacritic and base learner online while solving a single task.
Our strategy is thus related to the metaloss learning in EPG (Houthooft et al., 2018) , but learned online rather than offline, and integrated with Off-PAC rather than their on-policy policy-gradient learning.
The most related prior work is LIRPG (Zheng et al., 2018) , which meta-learns an intrinsic reward online.
However, their intrinsic reward just provides a helpful scalar offset to the environmental reward for on-policy trajectory optimization via policy-gradient (Sutton et al., 2000) .
In contrast our meta-critic provides a loss for direct actor optimization just based on sampled transitions, and thus achieves dramatically better sample efficiency than LIRPG reward learning in practice.
We evaluate our framework on several contemporary continuous control benchmarks and demonstrate that online meta-critic learning can be integrated with and improve a selection of contemporary Off-PAC algorithms including DDPG, TD3 and SAC.
We present Meta-Critic, an auxiliary critic module for Off-PAC methods that can be meta-learned online during single task learning.
The meta-critic is trained to generate gradients that improve the actor's learning performance over time, and leads to long run performance gains in continuous control.
The meta-critic module can be flexibly incorporated into various contemporary Off-PAC methods to boost performance.
In future work, we plan to apply the meta-critic to conventional offline meta-learning with multi-task and multi-domain RL.

assistant: text: We present Meta-Critic, an auxiliary critic module for off-policy actor-critic methods that can be meta-learned online during single task learning.