E FFICIENT D EEP R EINFORCEMENT L EARNING R EQUIRES R EGULATING S TATISTICAL O VERFITTING Anonymous authors
Paper under double-blind review
A BSTRACT
Deep reinforcement learning algorithms that learn policies by trial-and-error must learn from limited amounts of data collected by actively interacting with the environment.
While many prior works have shown that proper regularization techniques are crucial for enabling data-efficient RL, a general understanding of the bottlenecks in data-efficient RL has remained unclear.
Consequently, it has been difficult to devise a universal technique that works well across all domains.
In this paper, we attempt to understand the primary bottleneck in sample-efficient
deep
RL by examining several potential hypotheses such as non-stationarity, excessive action distribution shift, and overfitting.
We perform thorough empirical analysis on state-based DeepMind control suite (DMC) tasks in a controlled and systematic way to show that statistical overfitting on the temporal-difference (TD) error is the main culprit that severely affects the performance of deep RL algorithms, and prior methods that lead to good performance do in fact, control the amount of statistical overfitting.
This observation gives us a robust principle for making deep RL efficient: we can hill-climb on a notion of validation temporal-difference error by utilizing any form of regularization techniques from supervised learning.
We show that a simple online model selection method that targets the statistical overfitting issue is effective across state-based DMC and Gym tasks.
I NTRODUCTION
Reinforcement learning (RL) methods, when combined with high-capacity deep neural net function approximators, have shown promise in domains such as robot manipulation (Andrychowicz et al., 2020),
chip placement (Mirhoseini et al., 2020), games (Silver et al., 2016), and data-center cooling (Lazic et al., 2018).
Since every unit of active online data collection comes at an expense (e.g., running real robots, chip evaluation using simulation), it is important to develop sample-efficient deep RL algorithms, that can learn efficiently even with limited amount of experience.
Devising such efficient RL algorithm has been an important thread of research in recent years (Janner et al., 2019;
Chen et al., 2021;
Hiraoka et al., 2021).
In principle, off-policy RL methods (e.g., SAC (Haarnoja et al., 2018), TD3 (Fujimoto et al., 2018),
Rainbow (Hessel et al., 2018)) should provide good sample efficiency, because they make it possible to improve the policy and value functions for many gradient steps per step of data collection.
However, this benefit does not appear to be realizable in practice, as taking too many training steps per each collected transition actually harms performance in many environments.
Several hypotheses, such as overestimation (Thrun & Schwartz, 1993; Fujimoto et al., 2018), non-stationarities
Lyle et al., 2022), or overfitting (Nikishin et al., 2022) have been proposed as the underlying causes.
Building on these hypotheses, several mitigation strategies, such as model-based data augmentation (Janner et al., 2019), the use of ensembles (Chen et al., 2021), network regularizations (Hiraoka et al., 2021), and periodically reseting the RL agent from scratch while keeping the replay buffer (Nikishin et al., 2022), have been proposed as methods for enabling off-policy RL with more gradient steps.
While each of these approaches significantly improve sample efficiency, the efficacy of these fixes can be highly task-dependent (as we will show), and understanding the underlying issue and the behavior of these methods is still unanswered.
In this paper, we attempt to understand why taking more gradient steps can lead to worse performance with deep RL algorithms, why heuristic strategies can help in some cases, and how this challenge can be mitigated in a more principled and direct way.
Through empirical analysis with the recently proposed tandem learning paradigm (Ostrovski et al., 2021), we show that in the early stages of training, TD-learning algorithms tend to quickly overfit on the temporal-difference (TD) error (i.e., the error between the Q-network and the bootstrapping targets), reflected as a gap between the TD errors computed on the training set and a held-out validation set, and give rise to a worse final solution.
We further show that many existing methods devised for the data-efficient RL setting are effective insofar as they mitigate this statistical overfitting problem.
This insight gives a robust principle for making deep RL efficient: in order to improve data-efficiency, we can simply select the most suitable regularization for any given problem by hill-climbing on the validation TD error.
We realize this principle in the form of a simple online model selection method, that attempts to automatically discover the best regularization strategy for a given task during the course of online
RL training, that we call Automatic model selection using Validation TD error (AVTD).
AVTD trains several off-policy RL agents on a shared replay buffer where each agent applies a different overfitting regularizer.
Then, AVTD dynamically selects the agent with the smallest validation TD error for acting in the environment.
We find that this simple strategy alone often performs similarly or outperforms individual regularization schemes across a wide array of Gym and DeepMind control suite (DMC) tasks.
Critically, note that unlike prior regularization methods, whose performance can vary drastically across domains, our approach behaves robustly across all domains.
To summarize, our first contribution is an empirical analysis of the bottlenecks in sample-efficient deep RL.
We rigorously evaluate several potential explanations behind these challenges, and observe that statistical overfitting on the TD-error in the early stages of training is one of the biggest culprits that inhibits performance of data-efficient deep RL.
Our second contribution is a simple active model selection method (AVTD) that attempts to automatically select regularization schemes by hill-climbing on validation TD error.
Our method often matches or outperforms the best individual regularization scheme across a wide range of Gym and DMC tasks.
P RELIMINARIES A ND P ROBLEM S TATEMENT
The objective in RL is to maximize the long-term discounted return in a Markov decision process (MDP), ( S , A , P, r, γ ) , consisting of a state space S , an action space A , a transition dynamics model
P ( s ′ | s , a ) , a reward function r ( s , a ) , and a discount factor γ ∈ [0 , 1) .
The Q-function Q π ( s , a ) for a policy π ( a | s ) is the expected discounted reward obtained by executing action a at state s and following π ( a | s ) thereafter, Q π ( s , a ) :
=
E π [ (cid:80) ∞ t =0 γ t r ( s t , a t )] .
The optimal Q-function is achieved when it satisfies the Bellman equation: Q ⋆ ( s , a ) =
E s ′ ∼ P
s ′ | s , a ) [ r ( s , a ) + γ max a ′ Q ⋆ ( s ′ , a ′ )] .
Practical off-policy methods ( e.g. , Mnih et al., 2015; Hessel et al., 2018; Haarnoja et al., 2018) train a Q-network, Q θ (parameterized by θ ), to minimize the temporal difference (TD) error:
[Equation]
(1) where D is the replay buffer consisting of the transitions ( s , a , s ′ ) collected so far, ¯ Q is the target Qnetwork that is often updated to follow the Q-network Q θ with delay or smoothing (Fujimoto et al., 2018) so that the target does not move too quickly, and a ′ is usually drawn from a policy π ( a | s ) that can maximize or approximately maximize Q
θ ( s , a ) .
In theory, these off-policy algorithms can be made very sample efficient by minimizing the TD error fully over any data batch, which in practice translates to making more update steps to the Q-network per environment step, or higher “update-to-data” ratio (UTD) (Chen et al., 2021).
However, when done na¨ıvely, this can lead to worse performance (e.g., on DMC tasks (Nikishin et al., 2022) and on
MuJoCo gym tasks (Janner et al., 2019)).
There have been many prior methods proposed for dealing with high UTD issues (e.g., DroQ (Hiraoka et al., 2021), REDQ (Chen et al., 2021), and resets (Nikishin et al., 2022)).
However, we find that none of these prior methods and other simple baseline regularization schemes such as weight decay, dropout and spectral normalization (Miyato et al., 2018) work well across all the tasks (see
Appendix A, Figure 9).
What is the primary culprit that can explain the high UTD challenge?
Can we address it in a more direct and principled way?
T HE P RIMARY C ULPRIT B EHIND F AILURE OF H IGH UTD D EEP RL
In this section, we attempt to understand the underlying causes behind the failure of off-policy
RL algorithms in the high UTD deep RL and whether prior sample-efficient RL algorithms have addressed these problems appropriately.
We examine several plausible hypotheses that prior works posit: Q-value overestimation due to distribution shift (Fujimoto et al., 2019; Kumar et al., 2020), non-stationarity due to changing data distributions (Lyle et al., 2022), as well as early overfitting to the replay buffer (Nikishin et al., 2022).
We first describe the setup for our empirical analysis.
Then, in the next section, we demonstrate through a controlled study that the aforementioned hypothesized reasons are not sufficient to explain the challenges with high UTD.
Then, by demonstrating that high
UTD deep RL usually results in high generalization gap in the TD error, we argue that the main culprit behind the failure mode of high UTD learning is likely statistical overfitting.
We validate this hypothesis by evaluating some recently proposed regularizers, and show that these regularizers are effective insofar as they address statistical overfitting.
Experimental setup.
We first describe the setup for our analysis.
Many of the experiments in our empirical study utilize passive sources of data obtained from previous online RL runs.
We replay this data in different ways to control for and examine various hypotheses.
For generating this logged data, we utilize one run of a resetting SAC agent from Nikishin et al.
(2022), trained with a UTD value of 9.
We analyze a standard SAC agent in the high UTD regime.
Since we operate in the offline regime, to stabilize TD learning, we additionally normalize the features of the last layer (following prior works on TD stability (Bjorck et al., 2021a; Kumar et al., 2021a)).
We refer this as feature normalization ( FN ).
We added FN in the last layer of the Q-network in our analysis except DroQ, as it already utilizes LayerNorm.
For fair comparisons, we use feature normalization in all the experiments including the online setting in this section.
While we keep most of the hyperparameters the same, there are still some small differences between the online and offline settings.
In the online setting, we use the standard SAC which uses entropy backup in the bellman update.
In the offline setting, we remove the entropy term in the bellman backup and use deterministic backup (the mean of the action from the Gaussian actor is used).
Our analysis focuses on the fish-swim environment from DMC suite since high UTD training results in the largest gap in this domain (see the online column in Appendix B.1, Figure 10).
We obtain similar trends for many other experiments; a complete set of our analysis results are in Appendix B.1.
The confidence interval in our performance curves refers to the standard error computed over 8 random seeds.
See implementation details about different regularizers in Appendix B.
3. C AN POOR DATA COLLECTION , DISTRIBUTION SHIFT OR NON - STATIONARITY EXPLAIN THE FAILURE OF HIGH UTD LEARNING ?
First observe that, as expected, the performance of a standard SAC agent degrades as the UTD value increases (Figure 1- left ).
We will now attempt to understand if this performance degradation can be attributed to (a) poor data collection, (b) excessive action distribution shift and overestimation in the Q-function or (c) non-stationarity of the replay buffer.
(a) Quality of data used for training.
One might speculate that SAC behaves poorly in the high
UTD regime due to its inability to effectively collect exploratory data.
To understand if this might be the primary source of issues in high UTD learning, we analyze the behaviors of RL methods with high UTD in an offline setting, when training on identical data.
If indeed the negative effects of higher UTD ratios are entirely due to exploration and data collection, we would expect this change to greatly mitigate the bottlenecks with higher UTD ratios.
In this study, we trained SAC with different
UTD values on the aforementioned logged dataset, but replayed the data sequentially (following the tandem learning protocol (Ostrovski et al., 2021)).
This approach mimics how a typical online
RL agent would gradually observe data as it explores, but here, the dataset itself is independent of the agent being trained.
We refer this setting as the offline streaming setting.
As shown in Figure 1- middle left , the performance of SAC still degrades as UTD increases, even though the data comes from a high performing agent.
This suggests that the poor data collection alone does not explain the failure of high UTD learning.
Since, this setting still preserves the challenges of learning from data, including the effect of the training distribution and data quantity, we investigate these next.
(b) Non-stationarity in replay buffer data distributions.
Another potential explanation for the issues in learning with high UTD is non-stationarity: with higher UTD, the algorithm makes more gradient updates on the learned policy, allowing the distribution of the learned policy to change more drastically between iterations of learning.
Sudden changes in the data distribution and nonstationary target values of this sort have been regarded as challenges in online RL (Igl et al., 2020).
As before, to understand if high UTD challenges arise from non-stationarity, we construct an experiment that removes this factor.
We rerun SAC with different UTDs in the offline streaming setting from above, but now also reshuffle the buffer before training. That is, while the previous streaming
[Figure]
setting replayed data in order it was collected by the online RL agent, this new setting presents data sequentially, but not in the same order that it was collected.
This ensures that the data distribution of samples used for training is stationary and does not change over the course of training.
We refer this as the offline shuffled streaming setting.
Note however that the underlying RL algorithm still observes new data points as it trains for longer.
We still observe a similar performance trend in this shuffled streaming setting, as shown in Figure 1- middle right , indicating that non-stationarity of the data distribution alone also does not explain the failure of high UTD learning.
(c) Distribution shift and out-of-distribution (OOD) actions.
Our analysis so far suggests that the challenges in learning with high UTD are related to effective learning from passive data: even when the data quality and non-stationarity are accounted for, the performance with high UTDs is worse.
One might speculate that an obvious challenge for learning from data is action distribution shift or OOD actions (Fujimoto et al., 2019; Levine et al., 2020; Kumar et al., 2019): higher UTDs require more off-policy Bellman backups, resulting in backups from OOD actions, and Q-value overestimation (Thrun & Schwartz, 1993; Van Hasselt et al., 2016; Fujimoto et al., 2018).
Note that overestimation in the Q-function in general stems from multiple sources such as imperfect minimization of Bellman error, optimism due to OOD actions, and constraints imposed by the function class.
In this study, our goal is to investigate if OOD actions are an issue in the high UTD regime.
Hence, we plot the gap in Q-values at actions chosen by the policy and the actions in the dataset: ∆ Q = E s ∼D , a π ∼ π ( a | s )
[ Q θ ( s , a π )] − E s , a β ∼D [ Q θ ( s , a β )] (which measures how overestimated are the Q-values due to action distribution shift following (Kumar et al., 2020)).
By inspecting the Q gap (see Figure 1, rightmost and Figure 16 for other environments), we find that for UTD=1,3,9, the gaps are generally very similar to each other and for UTD=20, the gaps are higher but still controlled. Despite the similarity in the Q gaps for UTD=1,3,9, the performance is widely different.
Therefore, the performance degradation from ramping up the UTD cannot be explained due to action distribution alone.
Note that we are not claiming that action distribution shift is not a problem in general, but that our evidence shows that in the high UTD online RL settings that we study, distributional shift does not explain the performance difference.
This is perhaps expected as our dataset contains all the experience from an online RL run, and is hence of high coverage.
3. C AN STATISTICAL OVERFITTING EXPLAIN THE FAILURE OF HIGH UTD LEARNING ?
Even after using data of high quality obtained from the run of resetting SAC, and after correcting for non-stationarity and distribution shift, we find that the challenges with high UTD RL still remain.
This hints at the possibility that the actual underlying issue is statistical in nature, such as some form of overfitting to the data points that were used for training.
This sort of statistical overfitting should be identifiable by measuring errors on a held-out validation dataset.
We refer to this issue as “statistical overfitting” because it is a result of taking more gradient steps (i.e., higher UTD) with a fixed model class, mirroring the result of training with no early stopping in the supervised learning, where we observe statistical overfitting. However, it is important to note that overfitting is also distinct from the supervised learning case since TD learning does not have a static training objective. Consequently, this overfitting may not manifest necessarily as lower training errors, as training errors themselves query unseen action samples.
As shown in Figure 2, the validation TD error tends to be correlated with the failure cases with high UTD.
Note that the validation TD error also correlates well with the increase of UTD ratio, demonstrating that the degradation in performance is likely, at least, related to statistical overfitting during training.
We also remark that our hypothesis of statistical overfitting is distinct from prior works: while Nikishin et al.
(2022) utilizes the term “overfitting” to collectively refer to the challenges in high UTD learning, this prior work does not use a held-out validation set for their analysis, which makes it impossible to conclude if the challenges are due to statistical overfitting on the samples in the training dataset or some other factor. [Figure]
We have shown empirical evidence that statistical overfitting is the most plausible explanation for the failure case of high UTD learning on fish-swim , but how about other environments?
It turns out that most other DMC tasks that suffer from the high UTD learning issue also has the same trend (see Figure 12 in Appendix B.1).
This suggests that the biggest challenge that needs to be handled in such data-efficient deep RL settings is that of statistical overfitting on the TD error
[Figure]
[Figure]
V a li d a t i o n T D E r r o r , L v a li d ( )
[Figure]
We include a more complete set of results in Appendix B
1, Figure 13 (Online), Figure 15 (Offline Shuffled)
3. C AN M ITIGATING S TATISTICAL O VERFITTING E XPLAIN THE G OOD P ERFORMANCE OF P RIOR R EGULARIZERS ?
We provided empirical evidence in the previous section that statistical overfitting is the most plausible explanation for the failure of na¨ıve RL methods with high UTD, compared to a number of other previously hypothesized explanations.
In this section, we attempt to understand if the performance improvements from a variety of previously proposed regularizers, can be attributed to their effectiveness in mitigating statistical overfitting.
We note that none of the methods we study enable high UTD learning across all tasks (as we have previously discussed), so our study instead focuses on understanding whether methods that work well in each setting also overfit less statistically.
These regularizers include dropout (Gal & Ghahramani, 2016)
( DO , used by Hiraoka et al.
(2021)), weight decay (Loshchilov & Hutter, 2017) ( WD , used by Lillicrap et al. (2015)), spectral normalization (Miyato et al., 2018) ( SN , used by Gogianu et al. (2021); Bjorck et al. (2021b)), periodic resets (Nikishin et al., 2022), and a combination of LayerNorm (Ba et al., 2016) and dropout ( DroQ (Hiraoka et al., 2021)).
All of these regularizers operate differently: dropout injects stochasticity into the Q-network, weight decay controls the parameter norm; spectral normalization controls the maximum singular value of the weight matrix.
We observe that SAC exhibits lower validation
TD errors when trained with these regularizers in the high UTD regime (as shown in Figure 3 for fish-swim and Appendix B.1, Figure 15 for other environments).
This further highlights that a reduction in statistical overfitting on the TD-error does correspond to better performance.
We would also highlight that the regularizers that achieve the lowest validation TD error offline are usually one of the top performing methods online (Figure 4), hinting that the issues that these regularizers addressed could be mostly statistical overfitting.
A UTOMATIC M ODEL S ELECTION B ASED O N V ALIDATION TD (AVTD)
The performance of various regularization methods above indicates that no single regularizer performs well on all the tasks.
More so, it is also unreasonable to expect that a single regularizer would perform well on every deep RL problem.
However, if we can devise a general principle that allows us to automatically identify a good regularization approach from among a set of candidate approaches, we would expect such a principle to perform well given a broad set of regularization methods.
Previously, we observed that the validation TD error of different regularization approaches correlates well with performance in the offline setting.
Can we somehow use this correlation to our advantage and select the best regularization approach automatically?
A na¨ıve approach that directly follows from our analysis would train multiple independent agents with different regularizers in parallel, for a small number of initial steps, then select the one with the smallest validation TD error and use it for the rest of training.
While intuitive, this approach may not necessarily work: TD error depends on the scale of the reward function, and typically as an online RL agent makes progress towards maximizing reward and observes higher reward value,
TD error increases.
This means that this na¨ıve approach will select the agent that has made the least progress towards maximizing reward as it is likely to be the undesirable one that attains the smallest TD error.
To address this shortcoming, we consider a simple modification of this idea: we instead train multiple agents with different regularizers on a shared replay buffer, such that the data collection does not confound the evaluation of TD error.
At each environment step, AVTD picks the agent with the lowest validation TD error to take actions in the environment.
Essentially, all the agents are utilizing the same buffer, similar to the offline streaming setting, except that the active agent (the agent that is taking action currently) collects data that goes into the replay buffer.
As we will show, this does not reduce the correlation between the validation TD error and the performance, and this selection strategy can reliably select the best performing algorithm without incurring the additional sample complexity that might result from running multiple learners in sequence to pick the best one.
An overview is shown in Algorithm 1.
E XPERIMENTAL E VALUATION OF AVTD
The goal of our experiments is to validate the principle that hill-climbing on validation TD error to mitigate statistical overfitting can improve performance in data-effcient deep RL.
To this end, we evaluate our active model selection method, AVTD along with previously-proposed regularization strategies for comparisons.
Through experiments, we will establish that automatically selecting the regularization strategy (or strength) via AVTD is able to match or outperform the best individual strategy.
Concretely, we will answer the following questions: (1) Is AVTD able to select the best regularization coefficient online out of a set of candidates?
, (2) How important is utilizing a validation set in AVTD? [Figure] and (3) Does AVTD match or improve the performance over the best performing regularization approach it must select from?
We first present answers to questions (1) and (2) and then present our final results in (3) .
Implementation details are in Appendix B.
[Figure]
(1) Is AVTD able to select the best regularization strength online?
To answer this question, we use five DroQ agents with different dropout rates (0 . 003 , 0 . 01 , 0 .
and evaluate if
AVTD is able to select the best dropout rate for each task independently.
We show in Figure 5 that
AVTD can reliably match the performance of the best regularizer on the four Gym tasks we train on, without apriori knowing which coefficient would perform well.
One might argue that simply training an ensemble of these coefficients could achieve a similar effect.
We show that this is not the case in Figure 6 by comparing to the uniform selection strategy where a randomly selected agent is used to act in the environment for any given rollout.
(2) Is there any benefit to specifically using validation TD error in AVTD?
To answer this question, we performed a study where we automatically adjust the regularization strategy by hill climbing on the training TD error instead of the validation TD error.
On fish-swim , we observe that utilizing validation TD error is critical, and training TD error leads to worse performance (Figure 7).
Qualitatively, we observe that the regularization strategy selected by the hill climbing on training TD error is the one that does not add any regularization, resulting in worse performance.
This demonstrates that the principle of hill climbing on the validation TD error is more robust than hill climbing on the training TD error, further corroborating the insights from our empirical analysis.
(3) Can AVTD match or exceed the performance of individual regularizers that it dynamically selects from, across a wide range of tasks?
To evaluate overall performance of AVTD in comparison with each individual regularizer, we evaluate AVTD, individual regularizers, and other prior methods on 9 DMC tasks and 4 MuJoCo
Gym tasks.
The comparative evaluation of AVTD and other methods is shown in Figure 8.
For AVTD, we use a combination of five regularization strategies: LayerNorm, LayerNorm + WD with a weight of 0 .
01 , WD with a weight of 0 .
01 alone, and LayerNorm + Dropout with fractions of 0 .
03 or 0 .
This set of regularizers includes at least one regularizer that performs well on each of the tasks (e.g., DroQ regularizers work well on Gym tasks; weight decay works well on DMC tasks).
However, no single strategy performs well across all the tasks.
The goal of AVTD is to identify the best performing method, and preferably improve it in each case.
To interpret the performance of AVTD, we also plot an oracle upper bound, that identifies the best regularization method for every task with unlimited on the fly access to the run of each regularizer.
AVTD frequently matches the best performing method (with the exception of the
DMC acrobot-swingup task) and, in the case of the hardest task ( humanoid-run ), outperforms prior methods, indicating that selecting the regularizer based on validation error is consistently effective.
Observe that AVTD closes the gap between the best individual regularizer (in this case,
WD=0.01) and this oracle approach by 30%, indicating that it is effective. [Figure] [Figure]
Average algorithm rank:
To further understand the efficacy of AVTD in selecting the best regularizer, we rank each of the individual regularization techniques and AVTD in terms of the average return obtained in the first 300K steps for all the tasks and compute the average rank attained by every approach.
A more effective regularization approach across the board should attain a smaller rank (ideally, close to 1.0).
As shown in Table 1, all prior regularizers exhibit statistically overlapping values of average rank, indicating that none of the methods is the best across the board.
On the other hand, AVTD attains an average rank of 2.923, improving over all the other methods significantly.
This indicates the efficacy of AVTD in attaining good performance across the board.
R ELATED W ORK
In image-based RL domains, prior works have identified overfitting issues (Song et al., 2019) and found data augmentation to help (Kostrikov et al., 2020; Yarats et al., 2021; Raileanu et al., 2021).
Cetin et al.
(2022) identified a “self-overfitting” issue that is caused by TD learning with a convolutional encoder and low magnitude rewards.
Our work is distinct as we mainly focus on state-based tasks with mostly dense rewards.
Overfitting is also studied in offline RL (Kumar et al., 2021b;
Arnob et al., 2021; Lee et al., 2022), and while we do run some analysis in offline RL, we follow the tandem learning protocol (Ostrovski et al., 2021), where the offline dataset is generated via an active
RL agent and is not an arbitrary distribution.
In the sample-efficient deep RL setting that we study in this paper, Nikishin et al.
(2022) observed that forcing the TD learning to fit on limited initial data with many gradient steps can hinder the learning progress later on in the training.
This prior work speculates that this observation could be due to some “overfitting-like” phenomenon, however, it does not characterize what this overfitting precisely means and shows no evidence of statistical overfitting.
This prior work also does not utilize any notion of a held-out validation set, which we believe is essential for quantifying any form of statistical overfitting.
Finally, our analysis also examines the feasibility of various other hypotheses (e.g., non-stationarities of the replay buffer (Lyle et al., 2022; Igl et al., 2020), action distribution shift (Fujimoto et al., 2019), value under/overestimation (Fujimoto et al., 2018; Chen et al., 2021;
Wang et al., 2021)) towards explaining issues in data-efficient deep RL, but we find that statistical overfitting is the primary culprit.
Regularization in deep RL.
Regularization schemes, such as dropout (Gal & Ghahramani, 2016), layernorm (Ba et al., 2016), or batchnorm (Cheng et al., 2016) have been effective in improving the sample efficiency of deep RL algorithms.
For example, Hiraoka et al.
(2021) uses dropout and lay- [Figure]
[Table] [Figure]
WD=0.
[Figure]
DroQ=0. ernorm on top of SAC to attain near state-of-the-art performance on MuJoCo gym Liu et al.
(2019) found that L 2 weight regularization on actors can improve both on-policy and off-policy RL algorithms.
Nikishin et al.
(2022) propose periodic resets of critic weights, and can also be interpreted as a form of regularization.
Despite the empirical successes of these regularization approaches, the understanding of the principle behind these regularization approaches is lacking.
Our analysis sheds light on the connection of these regularization approaches to statistical overfitting.
We also observe that the efficacy of these regularizers is quite domain dependent: not all regularizers work in all domains (see Figure 9).
On the contrary, we do not propose yet another regularizer, but a method to select from among regularizers.
Our method, AVTD, is also related to theoretical algorithms that attempt to do online model selection (Foster et al., 2019; Lee et al., 2021; Cutkosky et al., 2021), that study this problem from a theoretical perspective.
Khadka et al.
(2019) also utilizes multiple learners and actively selects from them based on an estimate of return, distinct from validation TD-error.
D ISCUSSION
In this work, we attempted to understand the primary bottlenecks in data-efficient deep RL.
Through a rigorous empirical analysis, we showed that poor performance in high UTD deep RL is often correlated with statistical overfitting, and the effectiveness of many existing regularizers can be explained by their ability to address overfitting.
We use this experimental design to devise a principle for obtaining sample-efficient deep RL: by targeting this overfitting issue by an active model selection strategy, that automatically adjusts regularization based on validation TD-error, we can often match the best and outperform existing regularizers on each task, achieving better overall performance.
While AVTD can work well across a number of domains, several important questions remain.
For instance, it is not clear why and when certain regularization strategies work better than others.
If we can answer this question, we can optimize for validation TD error in a more straightforward fashion without requiring multiple parallel agents.
This likely would require understanding the learning dynamics of TD-learning, which is an interesting topic for future work.
Reducing the computational cost of our model selection approach is also an interesting avenue for future work.
Appendices A F AILURE C ASE OF E XISTING R EGULARIZERS
[Figure]
B I MPLEMENTATION D ETAILS
AVTD.
In all our experiments, we use ε = 0 .
1 unless specified otherwise.
This means that at each environment step, there is a 10% chance that a random agent is picked and the action is sampled from that random agent.
One held-out episode of transitions is collected after every 10 episodes where the actions are picked with the same strategy above.
These environment steps are also counted towards the number of steps taken by the AVTD for fair comparisons.
Weight decay (WD).
For all our experiments with weight decay, we apply AdamW (Loshchilov & Hutter, 2017) on the weight matrices of the Q -network (not on bias) except the last layer of the network (that maps the last layer feature to a scalar).
When LayerNorm and weight decay are used together, weight decay is not applied on the bias and the scale learned in the LayerNorm.
Unless specified otherwise, we use a weight decay coefficient of 0 . 01 .
Spectral normalization (SN).
For spectral normalization, we follow the implementation of
Gogianu et al.
(2021) where we use 1 power iteration to keep a running estimate of the singular vector (that corresponds to the largest singular value) and backpropagate through the norm.
We follow the best-performing setting in Gogianu et al.
(2021) where SN is only applied to the penultimate layer of the Q -network (the layer that has the 256 × 256 weight).
LayerNorm (LN).
For all our experiments with LayerNorm (Ba et al., 2016), we use it right before each ReLU activation in the Q -network and learns additional per-feature-element scales and biases.
Feature Normalization (FN).
For all our experiments with feature normalization, we use it right before the last layer of the Q -network where it is parameterized as
[Equation]
where w is the last layer weight of the Q-network and f θ ( s , a ) gives the post-activation feature right before the last layer.
This trick has been applied in many prior works to improve the stability of TD learning (e.g., (Bjorck et al., 2021a; Kumar et al., 2021a)).
Dropout (DO).
For all our experiments with dropout, we apply it in the Q-network before the
ReLU activation (before LayerNorm when combined together, e.g., DroQ (Hiraoka et al., 2021)).
Unless specified otherwise, we use a dropout rate of 0 .
03 for DO and 0 .
01 for DroQ.
Our DO implementation follows the open-source implementation of DroQ in Smith et al.
( https: //github.com/ikostrikov/walk_in_the_park ).
On DMC tasks, we turn off the policy delay in the DroQ baseline to keep it consistent with other baselines (e.g., Reset, weight decay) as they all do not use policy delay.
Reset.
For our experiments with Reset (Nikishin et al., 2022), we use the same strategy as the original paper where we re-initialize the agent from scratch periodically while keeping the replay buffer.
For DMC tasks, we use a reset frequency of 200K steps (same as the original paper).
For gym tasks, we use a reset frequency of 100K steps.
To our surprise, resetting every 100K could already match the performance of DroQ (Hiraoka et al., 2021).
Gym experimental setup.
For all the experiments on Gym tasks, we follow DroQ (Hiraoka et al., 2021) where we update the actor once per every 20 critic update steps and run 3 × 10 5 environment steps.
We use a warm-up period of 5000 steps where random actions are taken before updating the agents.
We use a UTD ratio of 20 (also used in DroQ (Hiraoka et al., 2021) and RedQ (Chen et al., 2021)).
DMC experimental setup.
For all the experiments on DMC tasks, we use a UTD ratio of 9, warm-up period of 10000 steps where random actions are taken before updating the agents, and run 10 6 environment steps.
Unless specified otherwise, no policy delay is used for experiments on DMC (actor update frequency is the same as the critic update frequency).
SAC.
For the SAC implementation used in this paper, we build our code on top of the jaxrl codebase: https://github.com/ikostrikov/jaxrl (Kostrikov, 2021).
The actor action distribution is parameterized by a Tanh-transformed diagonal Gaussian with learnable and statedependent mean and log standard deviation.
Both actor and critic ( Q -function) networks are initialized with orthogonal initialization with a multiplier of √ 2 , following the implementation in https://github.com/evgenii-nikishin/rl_with_resets (the official repository of Reset (Nikishin et al., 2022)).
The hyperparameter used for SAC is attached as follows (see
Table 2):
[Table]
Evaluation return computation.
Unless specified otherwise, the return for individual seed throughout the paper is estimated by running the policy with the deterministic mode (e.g., taking the mean of the Gaussian distribution for each action) for 10 independent trials.
B. DMC A NALYSIS
[Figure]
DMC tasks .
All agents use feature normalization in the last layer feature to stabilize TD learning.
Among all the tasks considered, almost all tasks exhibit the failure mode of high UTD in the online setting except on hopper-hop where UTD= performs the best.
In the offline setting, the performance degrade trend is cleaner where the agents trained with UTD=1 performs the best across the board (except on hopper-hop on the streaming setting, humanoid-run on the shuffled streaming setting, and finger-turn hard on both offline settings.) and the agents trained with UTD=20 performs the worst across the board (except on quadruped-run on shuffled streaming setting and finger-turn hard on both offline settings).
[Figure]
[Figure]
normalization
[Figure]
FN
FN + DO
FN + WD
FN + SN
FN + Reset
DroQ
Among all the tasks considered, fish-swim , humanoid-run and hopper-hop have the most similar relative performance ordering.
On humanoid-stand , all the other methods except the base SAC + FN correlates have similar performance ordering across online/offline settings.
On quadruped-run , we observe that the performance gap is much bigger in the offline settings, but the relative ordering of DO, WD, Reset and DroQ is roughly preserved (FN and FN + SN are much worse in the shuffled streaming setting).
The ordering is the most ambiguous in hopper-stand .
[Figure]
[Figure]
[Figure]
[Figure]
Environment Steps (×10 6 )
Q hopper-hop 0.
Environment Steps (×10 6 )
Q humanoid-run 0.
Environment Steps (×10 6 )
Q hopper-stand 0.
Environment Steps (×10 6 )
Q quadruped-run 0.
Environment Steps (×10 6 )
Q humanoid-stand 0.
Environment Steps (×10 6 )
Q finger-turn_hard
UTD= UTD=
UTD= UTD=
[Figure]
B. F ULL R ESULTS FOR AVTD
Aggregated performance computation. To compute the aggregated performance for each method, we use the following protocol – For each environment, we normalize the return by the best average return achieved on each task (taking the maximum over all agent and all environment steps and the average over all eight seeds).
After obtaining the normalized return for each environment, method and seed, we aggregate them over nine DMC tasks and four Gym tasks to obtain the sample efficiency curve for the aggregated normalized score following Agarwal et al.
Since
DMC experiments were run for a larger number of steps ( 10 6 ) than Gym experiments ( 3 × 10 5 ), we only take the performance of the DMC for the first 3 × 10 5 steps to compute the aggregated normalized score
[Figure]