Discovering Temporally-Aware Reinforcement Learning Algorithms

We would like to thank the reviewer for their thoughtful and insightful review. We are glad the reviewer finds our work “well-motivated and novel”, with “compelling visual representations” and “meticulous” experiments. The reviewer mentions several good points that we would like to address. ## Novelty of antithetic task sampling You are correct, using antithetic sampling for ES is not a novelty (Salimans et al., 2017). However, the update we propose in (12), “antithetic task sampling”, is designed to reduce the variance from applying ES in the multi-task setting. Using the update from Salimans et al. (2017), each candidate is evaluated on a randomly sampled task, before a rank transformation is applied to their fitness. This can lead to instability in the update, when the fitness across tasks has varying scales. In (12), we propose evaluating each antithetic candidate pair *on the same task*, before applying a rank transformation over the pair (equivalent to selecting the higher-performing candidate). This allowed us to normalize fitness across tasks, which we found led to faster meta-training convergence and improved final performance. ## Ablation of antithetic task sampling We do not ablate antithetic task sampling in the paper since it is tangential from the focus of the work. However, we include it since it is a novel and impactful implementation detail. We note that ES with antithetic task sampling is applied to both LPG and TA-LPG in all experiments (other than the meta-gradient model), so the ablation of temporal information is independent of this detail and rigorously demonstrates the impact of temporal information. ## Hyperparameters This is a good discussion point. Our reasoning for setting entropy=$0.0$ is based on [OpenAI's original PPO implementation](https://github.com/openai/baselines/blob/master/baselines/ppo2/defaults.py), which uses that setting for continuous control. [Extremely thorough follow-up work](https://arxiv.org/abs/2006.05990) (See Decision C32, Figure 77) [1] has found no evidence that entropy significantly improves performance on continuous control tasks. While we can tune this coefficient per-environment, we believe that this is against the spirit of the benchmark and is not commonly done. For a more in-depth discussion of this, we recommend [this blog post](https://iclr-blog-track.github.io/2022/03/25/ppo-implementation-details/) [2]. Nonetheless, we have run the requested set of experiments and have done a hyperparameter sweep over the entropy coefficient in similar settings to [1] with 5 seeds over 5 values and have attached the results to the supplementary material in Figure 9. In general, our findings align with [1] and we find that an entropy coefficient of 0.0 performs comparably to the others. While an entropy coefficient of 0.005 performs significantly better in Walker2d, it performs significantly worse than 0.0 in Ant and Humanoid. If the reviewer believes this would significantly improve the analysis of our paper, we can provide updated figures that tune the coefficient per-environment and per-algorithm. [1] Andrychowicz, Marcin, et al. "What matters for on-policy deep actor-critic methods? a large-scale study." International conference on learning representations. 2020. [2] Huang, et al., "The 37 Implementation Details of Proximal Policy Optimization", ICLR Blog Track, 2022. --- *We hope that most of the reviewer’s concerns have been addressed and, if so, they would consider updating their score. We’d be happy to engage in further discussions.*

We would like to thank the reviewer for their clear and useful review. We are glad the reviewer finds our work to be “simple and effective” and “supported by solid experiments and detailed analysis”. The reviewer brings up many good suggestions and questions we would like to address. ## Time Limits in RL We would like to thank the reviewer for pointing out this line of related work. We have updated the manuscript to include the suggested paper. However, there is an important difference in the use of the term “time-step” between these works. In our work, “time-step” refers to the total training budget (i.e. a “global” time-step). For the mentioned work, “time-step” refers to the time-step *within* an episode. We’ve further updated the manuscript to clarify this. Even with this distinction, we agree that incorporating time step information is not novel in RL. Any learning rate schedule incorporates global time-step information. However, incorporating time-step information in RL algorithm discovery methods (e.g. LPG and LPO) is novel, and leads to the significant improvements in performance demonstrated in our work. ## Ablation on the input Thank you for raising this question, we have included a discussion of alternative representations in the revised paper and are running the ablations outlined below. For LPG, our choice of representation was fairly arbitrary. We decided to include $\log(N)$ as a measure of total training budget - applying a logarithmic transformation in order to handle large values - and $n/N$ as a measure of training progress that would be invariant to $N$. We did not condition on $N$ or $n$ directly, since these numbers can be very large (e.g. $1e7$ for Min-Atar) and lead to dramatically out-of-distribution values when transferring to much longer or shorter horizons. As long as we have a measure of both total and relative train step, and apply suitable transformations, we are confident that the representation of total and relative train step will have a negligible impact on performance. To verify this, we are rerunning the experiments and will provide results with alternative parameterisations for training progress - $\log(N-n)$ and $(\log(N), \log(n))$ - in addition to another experiment directly conditioning on the total train steps, $N$. > Would adding $\log(N)$ to TA-LPO decrease performance? Since TA-LPO is trained on a single task with a constant $N$, $\log(N)$ would simply be a constant bias term. Therefore, adding $\log(N)$ to TA-LPO would be unlikely to impact in-distribution performance. However, including $\log(N)$ could affect transfer to out-of-distribution tasks with different $N$, since the input would then be out of distribution. > Figure 2 typo Thank you! We’ve fixed this in our updated manuscript. --- *We hope that most of the reviewer’s concerns have been addressed. We’d be happy to engage in further discussions.*

We would like to thank the reviewer for their very thorough and detailed review. We are glad that the reviewer finds that our experiments are systematic and show the strength of our method. The reviewer brings up several good points and questions that we would like to address. ## On theoretical justifications We’ve included a theoretical justification and proof in Appendix E. The high-level justification is that without temporal awareness, the algorithm cannot effectively trade off exploration and exploitation. For example, in the case of multi-armed bandits, the agent should converge to a single lever at the end of training, but perform exploration during training. ## On “careful” augmentations For LPG, our choice of augmentation was arbitrary. We decided to include $\log(N)$ as a measure of total training budget - applying a logarithmic transformation in order to handle large values - and $n/N$ as a measure of training progress that would be invariant to $N$. As long as we have a measure of each of these quantities and are scaled to a reasonable range, we expect the representation of total and relative train step to have a negligible impact on performance. To verify this, we are rerunning the experiments and will provide results with alternative parameterisations for training progress - $\log(N-n)$ and $(\log(n))$ - in addition to another experiment directly conditioning on the total train steps, $N$. > Would you explain the problem if $n/N$ and $\log(N)$ are added [to TA-LPO]? For TA-LPO it is *slightly* more involved. Given a quick understanding of the theoretical framework of LPO, TA-LPO is a simple augmentation. The theoretical framework behind LPO is described in Section 3.3. The key takeaway from is that the network needs to output $0$ when the likelihood ratio $p$ is equal to $1$. The network used for LPO has no biases and uses a tanh activation, so if the input is $0$, then the output is $0$. Thus, the input to the LPO network, $x_{r,A}$, is designed to be $0$ when $p=1$ (Equation 7). If we simply append $n/N$ as an input to TA-LPO, then the requirement doesn’t hold since it is not $0$ when $p=1$. Thus, we multiply $n/N$ by $x_{r,A}$ (which is $0$ when $p=1$). We do not include any variant of $\log(N)$ because LPO is only trained with a single $N$, which would simply reduce that term to a bias term. We believe this is an insignificant challenge for future work and does not reduce the strength of our contribution. ## Questions: > $T$ is not explained Thank you for catching this. $T$ is the trajectory/rollout length that the actor collects each update step, not the total number of environment interactions $N$. We have updated the manuscript to include this! > Is $n/N$ unbounded when $N$ is unbounded? Would you explain $N$ and provide an example task? $N$ is the total number of environment interactions we provide to the agent to learn. For example, in MinAtar-Breakout, the agent interacts with the environment for $1e7$ timesteps, so $N=1e7$. From this, we calculate $n/N$, which measures the proportion through training, and $\log(N)$, which provides the agent with the total number of training steps. When $N$ is unbounded, $n/N$ is a constant $0$. In practice, the total training budget $N$ is usually known, as this allows RL algorithms to trade off exploration over training. > Would you explain "this stabilized training" in detail? Thank you for pointing this out, we have revised the paper to make this clearer. The update we propose in (12), “antithetic task sampling”, is designed to reduce the variance from applying ES in the multi-task setting. Using the update from Salimans et al. (2017), each candidate is evaluated on a randomly sampled task, before a rank transformation is applied to their fitness. This can lead to instability in the update, when the fitness across tasks has varying scales. In (12), we propose evaluating each antithetic candidate pair *on the same task*, before applying a rank transformation over the pair (equivalent to selecting the higher-performing candidate). This allowed us to normalize fitness across tasks, which led to faster meta-training convergence and improved final performance. We do not examine this rigorously in the paper since it is tangential from the focus of the work. However, we include it since it is a novel and impactful implementation detail, which we had to apply consistently throughout the LPG experiments. > Does it mean that three algorithms are implemented somewhere? Thank you for pointing this out! We have updated the manuscript to clarify this. We implemented LPG and LPO, which are successors to those papers. ## Misc: Thank you for catching the typo in equation 10 and the incorrect year on the reference! We’ve fixed these in the updated manuscript. --- *We hope that most of the reviewer’s concerns have been addressed and, if so, they would consider updating their score. We’d be happy to engage in further discussions.*