PID-Inspired Inductive Biases for Deep Reinforcement Learning in Partially Observable Control Tasks

Deep reinforcement learning (RL) has shown immense potential for learning to control systems through data alone. However, one challenge deep RL faces is that the full state of the system is often not observable. When this is the case, the policy needs to leverage the history of observations to infer the current state. At the same time, differences between the training and testing environments makes it critical for the policy not to overfit to the sequence of observations it sees at training time. As such, there is an important balancing act between having the history encoder be flexible enough to extract relevant information, yet be robust to changes in the environment. To strike this balance, we look to the PID controller for inspiration. We assert the PID controller's success shows that only summing and differencing are needed to accumulate information over time for many control tasks. Following this principle, we propose two architectures for encoding history: one that directly uses PID features and another that extends these core ideas and can be used in arbitrary control tasks. When compared with prior approaches, our encoders produce policies that are often more robust and achieve better performance on a variety of tracking tasks. Going beyond tracking tasks, our policies achieve 1.7x better performance on average over previous state-of-the-art methods on a suite of locomotion control tasks.

Paper

References (76)

Scroll for more · 38 remaining

Similar papers

Peer review

Reviewer RWrF6/10 · confidence 4/52023-07-03

Summary

The paper proposes two history encoders for RL in partially observable control tasks. The history encoders are designed with PID-inspired inductive bias. Specifically, the inductive bias comes from lifting the observation into features consisting of summation and difference of observation over the historical horizon, which are analogous to the integral and derivative of tracking errors in PID. It was shown that the proposed history encoders, especially the generalized PID encoder, could achieve better performance and robustness than GRU and transformers in tracking and locomotion tasks when integrated with RL algorithms.

Strengths

I particularly appreciate the new perspective presented by the authors in combining conventional control techniques with reinforcement learning. The idea of incorporating PID architecture into history encoders is interesting and novel to the best of my knowledge. The advantages of the generalized PID encoders over GRU and transformers, especially in the locomotion tasks, validate that the PID-inspired inductive bias is indeed effective in some control tasks. This paper could inspire the RL community to discover more powerful and generalizable architectures with insights from control theory and conventional control techniques.

Weaknesses

1. In lines 102-104, the authors stated: > > In the case of MIMO tracking problems, where there are M signals with M corresponding actuators, one can control the system with M separate PID controllers. However, this assumes there is a clear breakdown of which actuator influences which signal. > Decomposing a MIMO system into multiple SISO systems is indeed a practical way to synthesize MIMO PID controllers. However, there exist methods to directly synthesize PID controllers for MIMO systems without decomposition (e.g., [1]). While I am okay with the authors only comparing the proposed methods with a decomposed PID controller, the authors should appropriately assert the capacity of PID controllers based on the state-of-the-art literature. 2. The related work section should include a review of the literature on the combination of conventional control techniques with RL. For instance, there have been extensive efforts in tuning PID or learning an adaptive PID weight schedule with RL, which could be considered a special case of the control policy with the proposed PID encoder. I understand the paper is mainly targeting audiences from the RL community, but I think it is necessary to place the proposed method in the control literature as well. 3. While I am generally impressed by the experimental results, I am concerned about the failure of SAC-GPIDE in the HalfCheetah-V environment. It makes me wonder whether the PID-based inductive bias could limit the expressiveness of the policy network in some control tasks. For instance, I would doubt if the proposed method could still work when image-based observation is used. The authors do not provide any explanation or hypothesis for the failure in HalfCheetah-V. I would suggest providing more information and insights regarding it during the rebuttal and in the updated version of the paper. [1] Boyd, Stephen, Martin Hast, and Karl Johan Åström. "MIMO PID tuning via iterated LMI restriction." International Journal of Robust and Nonlinear Control 26, no. 8 (2016): 1718-1731.

Questions

1. Please see the three issues listed in the Weaknesses section. I would have a more positive impression of the paper if the authors could properly address these three issues during the rebuttal. 2. In addition, I want to ask the authors to clarify the role of attention heads in GPIDE. In the ablation study, the authors stated: > > It appears that the attention scheme for HalfCheetah is simply a poor reproduction of exponential smoothing, making it redundant and suboptimal. In fact, we found this phenomenon to be true across all attention heads and PyBullet tasks. We believe that the periodicity that appears here is due to the oscillatory nature of the problem and lack of positional encoding (although we found including positional encoding degrades performance). > If that is the case, does it mean that the attention heads could be simply replaced by exponential smoothing heads? It seems to be supported by the ablation study results (i.e., ES+SUM has similar or better performance than GPIDE with multiple types of heads). In lines 227-230, the authors said: > >This choice was not optimized but rather was picked so that all types of heads were included and so that GPIDE has roughly the same amount of parameters as our GRU baseline. > I don't think it is a good justification for the experimental design. The authors should attempt to find an optimized configuration so that the audience can have a better sense of the necessity of each proposed head, especially the attention head.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

2 fair

Presentation

3 good

Contribution

3 good

Limitations

The authors acknowledged the limitation of the proposed methods, which is the proposed PID-inspired inductive bias might not apply to all control tasks. While I personally doubt if the proposed method can ever be extended to systems with image-based observations, I do not think the authors are obligated to justify the feasibility of extension to visual control tasks in this paper. However, as suggested above, I do think the authors should provide more information and insights on the failure of GPIDE in Cheetah-V.

Reviewer 64AN6/10 · confidence 3/52023-07-03

Summary

The paper proposes a new, simplified architecture for reinforcement learning in the partially observable setting inspired by PID control. Through experiments on a number of tracking problems, and some locomotion environments, strong performance is obtained.

Strengths

- The exposition of the argument is very clear, even for a reader somewhat unfamiliar with some aspects. - Simplification of complex (and computationally expensive) recurrent architectures is a worthwhile endeavor. - Ablations are informative, and come with demonstrations of issues (Figure 4).

Weaknesses

- The largest weakness is in the evaluation. Most of the evaluation is devoted to low-dimensional tracking problems. The choice of state-based locomotion with only positions or velocities observable also seems a little artificial when there are many tasks that have existing sources of partial observability (long-horizon, first-person viewpoints). - One possibly beneficial use of an alternative state summary like GPIDE would be computational savings, but there isn't any measurement of that in the paper.

Questions

See the final weakness, it would be nice to see computational cost measured.

Rating

6: Weak Accept: Technically solid, moderate-to-high impact paper, with no major concerns with respect to evaluation, resources, reproducibility, ethical considerations.

Confidence

3: You are fairly confident in your assessment. It is possible that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.

Soundness

3 good

Presentation

3 good

Contribution

3 good

Limitations

Limitations are discussed.

Reviewer QQYm7/10 · confidence 4/52023-07-23

Summary

This paper considers history encoding for deep RL POMDP control problems through a PID-inspired lens. Specifically, authors introduce PIDE, a method of directly using PID control which extends to multiple-input multiple-output problems, and GPIDE, a PID-inspired encoder architecture. GPIDE consists of a series of heads that takes as input model observations and past history, and internally computes differences between observations (similar to the PID D-term) and aggregation/summation over all past timesteps (similar to the PID I-term). The method is then evaluated on tasks including mass-spring-damper, navigation, tolemak control, and pyBullet locomotion. Across these experiments, the method is compared against baselines of direct PID control, GRU, transformer, and several RL algorithms. GPIDE is found to have strong performance across both simple and complex tasks and be robust to domain transfer scenarios. Further ablation studies provide insight into design choices for GPIDE heads, visualize attention schemes, and evaluate a GRU+VIB baseline.

Strengths

#### Originality The ideas of the paper are generally original, building from prior deep RL work and focusing on the design of the feature encoder, especially designing a novel history encoding architecture which draws from PID controllers. The pieces of the architecture draw from general temporal aggregation principles and transformers. #### Quality The paper is generally high-quality. The experiments compare against relevant baselines and prior work, are run with multiple seeds, and the training / setup / tasks are clearly defined. The code is provided and looks cleanly written from initial observation, though I haven’t run it to verify. The ablation studies answer my initial questions about the architecture design, especially in how important the attention heads are. #### Clarity The manuscript is well written and clearly conveys the derivation of the method from PID controllers and explains the architecture and design choices in a very understandable way. Relevant figures are provided for context of the architecture and tasks. The experiments are well motivated and help understand the performance of PIDE / GPIDE across tasks, RL methods, and transfer scenarios. #### Significance GPIDE seems broadly applicable across deep RL control tasks, especially those related to tracking and navigation / locomotion as demonstrated by experiments. The method is an approach to handling the POMDP problem on control problems as a drop-in architecture for history encoding.

Weaknesses

#### Experiments Compared to RNNs such as GRU which consider only the current timestep and state to predict the next action, GPIDE seems to consider all past timesteps from 1 to t within each step, as part of the weighted summation resembling the PID I step, which may be more expensive than other methods if the time / observations are large. It may be worthwhile to consider potential inference time compute differences because of this, and also to consider ablations or baselines which also have such history context. #### Significance On line 116-117, the authors mention that LSTM, GRU, and transformers were shown to be powerful tools for NLP because of complex relationships within the task. Because control tasks may not have such complexities, such methods may overfit rather than help, especially in cases of domain transfer. However, these methods have also been applied to success in domains including robotics and visual encoding (e.g. https://arxiv.org/abs/2212.06817, https://arxiv.org/abs/2010.11929, https://arxiv.org/abs/2106.01345) - perhaps this indicates that the best targets for using GPIDE would be cases where highly-overparameterized / “large” models may overfit, which would be towards the simpler side.

Questions

#### Limitations The authors mention that control tasks which require memory may not be suitable - it would be further interesting to consider from the perspective of task similarity to that of PID control. Do the authors think that there would be correlation between similarity to PID / tracking tasks and successful application of GPIDE? For instance, a common image-based task would be visual grasping which involves reasoning about object geometry, where it may be less clear that results would directly transfer. Furthermore, some tasks may be less partially observable in nature than others - given this method focuses on a history encoder, would the relevance of history generally for certain tasks be relevant to consider?

Rating

7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

4 excellent

Presentation

4 excellent

Contribution

3 good

Limitations

The limitations are generally adequate (there are some questions in the section above).

Reviewer EZtX5/10 · confidence 4/52023-07-25

Summary

This paper proposes a new way to encode features in partially observable environments using PID. Experiments show superior results over several domains compared with recurrent and transformer encoders.

Strengths

The paper is easy to read overall. Experiments show promising performance on multiple domains.

Weaknesses

Some assumptions and technical details need to be clarified. 1) Using the difference between observations as the derivative of the error (D) is trivial, assuming that the reference value for the observation at different timesteps is the same, which is not true. 2) The author mentioned in Line 102 that using M separate PID controllers to control M signals has some clear shortcomings. This paper models the MIMO problem in a centralized manner, inputting all inputs and outputting a 3M dimensional vector. However, this would not be feasible if there is a large scale of signals that need to control. 3) It said the $f_{\theta}^h$ is a learnable linear projection, how to learn it is not discussed. Also with $g_{\theta}$. 4) How to determine the suitable length of the history, As for the length $1:t$ in $v_{1:t}^{h}$? More ablations should be provided. 1) The ablations investigate the influence of different types of heads, while why choosing these three settings (ES, ES+Sum, Attention) is not explained. What about ES+Attention? Why five ES + 1 Sum? Are there any insights in choosing the number and combination of different heads? 2) The influence of different lengths of history should also be investigated. More limitations should be discussed. For example, the encoder processing time is highly dependent on the length of the history. Some related works are not discussed in this paper. For example, [1-3]. [1] An adaptive deep reinforcement learning approach for MIMO PID control of mobile robots [2] Self-Tuning Two Degree-of-Freedom Proportional–Integral Control System Based on Reinforcement Learning for a Multiple-Input Multiple-Output Industrial Process That Suffers from Spatial Input Coupling [3] Robust Adaptive PID Control based on Reinforcement Learning for MIMO Nonlinear Six-joint Manipulator

Questions

Questions, Please see the pros and cons part about the assumptions, technical details, ablations, and limitations.

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

Please see the pros and cons part about the limitations.

Reviewer vEC95/10 · confidence 4/52023-07-27

Summary

This paper studies the problem of learning from histories in partially observable MDPs where a key question is how to design an architecture that is general enough so as to work on a large set of problems, yet specific enough to be sample efficient. Inspired by the success of PID in the more classical control literature, the idea here is to design an architecture that is solely comprised of summation, attention, and linear operations. Experiments show that on tracking problems, where PID is originally proposed for, as well as more complicated control problems, this simple architecture is good enough to achieve competitive results.

Strengths

The paper shows that using a complicated architecture is an overkill for many of the domains that the RL community considers as benchmarks. On this note I'd like to mention that, while the contexts are somewhat different, a similar conclusion can be made from "Towards Generalization and Simplicity in Continuous Control" Rajeswaran et al, where they show that simpler architectures such as linear models are equipped to deal with Mujoco Tasks. The difference is that in their paper they were considering reward-maximization in presence of the full state, whereas here the goal is learn a memory-like function in conjunction with performing well in the given task. In any case, I generally like results that show simple stuff work, because simple things are easy to understand, implement, and execute.

Weaknesses

Overall I like this paper but I also have some concerns: Fundamentally, I feel like the results in this paper are pertinent in terms of a bigger question, namely how rich we want our hypothesis class to be for learning a certain target. The solution adopted by the ML community nowadays seems to be: we really do not know how complicated a task is, so by choosing a very complicated architecture and the fact that we are at the mercy of universal function approximation capability, we can always in principle find the right fit. Moreover, the double descent phenomenon ("Deep double descent: where bigger models and more data hurt", Nakkiran et al) tells us that empirically we are very likely to find a good fit with larger and more complicated models and that, despite more classical belief, such an overparameterized fit happens to also be quite robust. ("A Universal Law of Robustness via Isoperimetry" Bubeck and Sellke) Now, moving to the RL setting, these insights from supervised learning do not really carry over because we usually learn by bootstrapping off of Bellman targets, and by increasing the complexity of our function approximator, we also have to learn from increasingly more complicated targets (unlike supervised learning where targets are fixed). So I think, at least with our current RL algorithms, unlike SL we always need to choose our function class carefully and so adding inductive bias, such as ones provided in this paper, can usually be helpful. My worry is that adding such biases are helpful in a limited sense: It is not clear how much inductive bias should I add for a given task when I don't know too much about that task. Sure, I can always choose environments and problem settings where I know that my inductive bias is conducive to solving the problem, but do we really want to bring back the burden to ML practitioners to carefully think about the kind of inductive biases that are useful for their task? Grounding my concerns more so in the experimental results provided here, for example we see that the inductive bias provided is already giving small (or negative) gains as we move to some of the more complicated domains such as HalfCheetah and Ant (based on Figures 18 and 19 in the Appendix), so I ask authors, are you not worried that as we move to much larger domains then it becomes increasingly more difficult to show performance gains for GPIDE compared to other approaches? In other words, does the inductive bias scale reasonably with problem complexity or there is only so much this could be useful? To further play devil's advocate, to say that GPIDE is capable of beating the transformer architecture is sort of a weird claim, because as authors say GPIDE could be thought of as a special case of transformers, and further as you show the attention layer is often not very useful. This tells me that with proper hyper-parameter tuning and regularization, the transformer architecture should in principle be able to always do better than GPIDE, and we can still hope to find the transformer useful as we move to larger problems.

Questions

I would like to ideally see an acknowledgment that as we move to much more difficult domains, GPIDE may be incapable of doing well simply because the actual function to be represented in not in the function class. But such an example is currently absent. This may give a false sense that the paper is claiming that GPIDE is a general-purpose memory learner but that is not true, and I am not saying that authors say it is true, but having examples of failure cases would really clarify this point. If I may say, I would also like to see experiments on different types of problems. For example, can we expect GPIDE to perform reasonably on image-based domains? Like the paper mentions, we can hope to apply the GPIDE on the embedding space learned by some more capable function approximator, but it seems to me that to learn good embeddings that are useful for downstream memory learning, one needs to leverage some kind of GRU/Transformer/LSTM architecture, and so it is not immediately clear to me how to leverage GPIDE in this setting. My other question is also that as we know RNNs struggle to learn important events from the distant past because the vanishing/exploding gradients. LSTMs and Transformers are less prone to this issue but I wonder if we could better compare this capability of GPIDE in contrast to the existing architectures. In the Half-Cheetah experiment, for example, do we have a good sense of how far back one needs to go to be able to accurately learn the position and/or the velocity signal? Also, from the intro the paper reads "Another hurdle stems from the fact that policies are often trained in an imperfect simulator, which is likely different from the true environment. Combining these two challenges necessitates striking a balance between extracting useful information from the history and avoiding overfitting to modelling error." My thoughts reading this sentence was that we are going to either have actual sim2real experiments or some kind of a transfer learning benchmark, where we learn the memory function in some settings, and test the learned memory function in another test setting. This would have been more convincing in terms of claiming that GPIDE is not prone to overfitting. Did I get it right that this experiment is absent?

Rating

5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.

Confidence

4: You are confident in your assessment, but not absolutely certain. It is unlikely, but not impossible, that you did not understand some parts of the submission or that you are unfamiliar with some pieces of related work.

Soundness

3 good

Presentation

3 good

Contribution

2 fair

Limitations

NA

Reviewer vEC92023-08-11

Awesome, thanks for the rebuttal. As alluded to by a few other reviewers (64AN RWrF), we still have a lingering question about scaling up GPIDE to larger domains, or domains with different inputs such as text or image. That said, I am really encouraged by your acknowledging that in the limitation section a more nuanced discussion on the potential limitation of this inductive bias would be highly appropriate. This would hedge against potentially over-claiming the result. This seems to be the kind of inductive bias that can a) work surprisingly well in lower dimensional settings and b) provide enough insights for follow up works to propose more scalable inductive biases. So overall, I keep my score and remain supportive of this paper getting accepted.

Reviewer 64AN2023-08-14

Thanks for your response, a couple of specific things below - **Computational savings**: I had a look at appendix E, and the details are only for training. While it's helpful, it would also be nice to get a sense of the inference costs for using GPIDE instead of baselines. For example, does it lead to a qualitative difference that lets some tasks run in real-time? This would be a significant win over baselines and I think is worth exposing. - **Low vs. high dimensional environments**: I'm not totally convinced by this line of argument. I believe the goal is to do research on interesting tasks. The most obvious existing case of partial-observability to me is something like a first-person viewpoint. I would also take strategic games that have fog of war (Stratego, Starcraft, etc.) as other good examples. Another great example is minesweeper. While some of these domains are very hard for existing algorithms, others seem to be quite natural and have been used by many papers in different subfields (first-person navigation in particular). Such domains seem to be much closer to the eventual deployment scenario of the paper's method than masked tracking problems, though I would be convinced by a good argument as to the deployment uses of tracking. I do acknowledge that I am not familiar with the literature, and using standard domains is a good idea.

Authorsrebuttal2023-08-15

Thank you for your reply! Your point about the test-time execution point is a good one that we had not considered during the writing of the paper, and we now realize that Appendix E does not fully shed light on this. As noted in our global response, we speculate that GPIDE without attention should be faster than a policy that uses GRU or LSTM; however, we cannot say for certain right now how much faster. We will work on creating a more efficient version of our code that assumes no attention is used to test this. We agree with you that research should be grounded in real, interesting applications. While the “fog-of-war” type of partial observability is interesting, we want to emphasize that there are many other types of partial observability worth studying, especially in robotic applications. For example, partial observability can come in the form of unknown system parameters (which are present in all of our tracking experiments) or unmeasured signals. While masking positions and velocities is one form of the latter that appears frequently in the literature, our tokamak control experiment has realistic assumptions on which states of the plasma can be measured in real time. Tokmak control using RL has gained attention from the community lately (e.g. see “Magnetic control of tokamak plasmas through deep reinforcement learning” from Degrave et al. which also considers a tracking problem), and this experiment highlights the partial observability challenges that this application faces.

Reviewer 64AN2023-08-15

I agree that the justification for Tokamak control seems stronger, but it is only a small portion of the experiments. I can also think of a task like landing rockets SpaceX-style, where precise measurements are not possible for cheap hardware, yet, for example, weight affects the control signal to be generated. This might be a bit more satisfying and natural than the given toy domains.

Reviewer RWrF2023-08-16

Thanks to the authors for the response! After reading the response and other reviewers' comments, I would like to keep my current score.

Program Chairsdecision2023-09-21

Decision

Accept (poster)

© 2026 NYSGPT2525 LLC