Offline Behavior Distillation
Authors: Shiye Lei
Sen Zhang
Dacheng Tao
Venue: NeurIPS 2024 poster (2024)
Keywords: Efficient Deep Learning
Dataset Distillation
Offline Reinforcement Learning
Primary area: optimization_for_deep_networks
TL;DR: We distill a large offline RL dataset into a few expert behavioral dataset for rapid policy learning.

Abstract: Massive reinforcement learning (RL) data are typically collected to train policies offline without the need for interactions, but the large data volume can cause training inefficiencies. To tackle this issue, we formulate offline behavior distillation (OBD), which synthesizes limited expert behavioral data from sub-optimal RL data, enabling rapid policy learning. We propose two naive OBD objectives, DBC and PBC, which measure distillation performance via the decision difference between policies trained on distilled data and either offline data or a near-expert policy. Due to intractable bi-level optimization, the OBD objective is difficult to minimize to small values, which deteriorates PBC by its distillation performance guarantee with quadratic discount complexity $\mathcal{O}(1/(1-\gamma)^2)$. We theoretically establish the equivalence between the policy performance and action-value weighted decision difference, and introduce action-value weighted PBC (Av-PBC) as a more effective OBD objective. By optimizing the weighted decision difference, Av-PBC achieves a superior distillation guarantee with linear discount complexity $\mathcal{O}(1/(1-\gamma))$. Extensive experiments on multiple D4RL datasets reveal that Av-PBC offers significant improvements in OBD performance, fast distillation convergence speed, and robust cross-architecture/optimizer generalization.

Offline Behavior Distillation
Shiye Lei
Sen Zhang
School of Computer Science
School Computer Science
The University of Sydney shiye. Leydnyd edu.
The University of Sydney sen. zhangdsydney edu. au
Dacheng Tao
College of Computing & Data Science Nanyang Technological University dacheng. tac@ntu. edu. ag
Abstract
Massive reinforcement learning (RL) data are typically collected to train policies offline without the need for interactions, but the large data volume can cause train- ing inefficiencies. To tackle this issue, we formulate offline behavior distillation (OBD), which synthesizes limited expert behavioral data from sub-optimal RL data, enabling rapid policy learning. We propose two naive OBD objectives, DBC and PBC, which measure distillation performance via the decision difference between policies trained on distilled data and either offline data near-expert policy. Due to intractable bi-level optimization, the OBD objective is difficult to minimize to small values, which deteriorates PBC by its distillation performance guarantee with quadratic discount complexity ( - 7) We theoretically establish the equivalence between the policy performance and action-valus weighted decision difference, and introduce action-value weighted PBC (Av-PBC) as a more effective OBD objective. By optimizing the weighted decision difference, Av-PBC achieves a superior distillation guarantee with linear discount complexity O 7))- Extensive experiments on multiple D4RL datasets reveal that Av-PBC offers sig- nificant improvements in OBD performance, fast distillation convergence speed, and robust cross-achiiecruuroopiiiizz generalization. The code available https: thub. com/LeavesLLee1/00)
Introduction
Due to the costs and dangers associated with interactions in reinforcement learning (RL., learning
policies from pre-collected RI. data has become increasingly popular [Levine al. 2020). Con-
sequently, numerous offline RL datasets have been constructed [Fu et al.) 2020] However, these offline data are typically massive and collected by sub-optimal or even random policies, leading to inefficiencies in policy training. Inspired by dataset distillation (DD) [Wang et al. 2018 Zhao et al.)
202T Lei and Tao, 2024], which synthesizes a small number of training images while preserving model training effeets, we further investigate the following question: Can distill vast sub-optimal RL data into limited expert behavioral data? Achieving this would enable rapid offline policy learning via behavioral cloning (BC) [Pomerlcau| 1991], which can (1) reduce the training cost and enable green AI; (2) facilitate downstream tasks by using distilled data as prior knowledge (e.g. continual RI.
[Gai et al. 2023), multi-task RL Yu et al. 2022]) ), efficient policy pretraining [Goecks al. 2019) ofiline-to-online fine-tuning (Zhao et al. )0:2)); and (3) protect data privacy (Qiao and Wang 2023
Unlike DD whose objective is prediction accuracy and directly obtainable from real data, the policy performance RL is measured by the expected return through interactions with environment. In an
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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offline paradigm, where direct interaction with environment is not possible, metric based on RL data necessary guide the RL data distillation. Therefore, we formalize the offline behavior distillation (OBD); a limited set of behavioral data, comprising (state, action) pairs, is synthesized from sub-optimal RI. data, so that policies trained on the compact synthetic dataset by BC can achieve small OBD objective loss, which incarnates high return when deploying policies in the environment.
The key obstacle for OBD is constructing a proper objective that efficiently and accurately estimates the policy performance based on the sub-optimal offline dataset, allowing for a rational evaluation of the distilled data. To this end, data-bat bata-based BC (DBC) and policy-based BC (PBC) present two naive OBD objectives. Specifically, DBC reflects the policy performance by measuring the mismatch between the policy decision and vanilla offline data. Leveraging existing offline RL algorithms that can extract near-optimal policies from sub- sub-optimal data [Levine et al., (0200, PBC improves upon DBC by correcting actions in offline data using near-optimal policy before measuring the decision difference. However, due to the complex bi-level optimization in OBD, the objectives are difficult to minimize effectively, resulting in an inferior distillation performance guarantee with the quadratic discount complexity (11((1 2) for PBC (Theorem lp. We tackle this problem and propose the action-valus weighted PBC (Av-PBC) as the OBD objective with superior distillation guarantee by taking inspirations from our theoretical findings. Concretely, we theoretically prove the equivalence between the policy performance gap and the action-valus weighted decision difference (Theorem 2). Then, by optimizing the weighted decision difference, we can obtain much tighter distillation performance guarantee with linear discount complexity (1/((1 - 7)) (Corollary D Consequently, weigh PBC with the simple action value, introducing Av-PBC as the OBD objective.
Extensive experiments on nine datasets of D4RL benchmark [Fu et al., 2020) with multiple envi- ronments and data qualities illustrate that our Av-PBC remarkably promotes the OBD performance, which is measured by normalized return, by 82.8% and 25.7% compared to baselines of DBC and PBC, respectively. Moreover, Av-PBC has a significant convergence speed and requires only quarter of distillation steps compared to DBC and PBC. By evaluating the synthetic data in terms of different network architectures and training optimizers, we show that distilled datasets possess decent cross cross-architeccin arcciiecturr/oppimiize performance. Apart from evaluations on single policy, we also investigate policy ensemble performance by training multiple policies on the synthetic dataset and combining them to generate actions. The empirical findings demonstrate that the ensemble operation significantly enhance the performance of policies trained Av-PBC-distille data by 25.8%.
Our contributions can be summarized as:
We formulate the offline behavior distillation problem, and present two naive OBD objectives of DBC and the improved PBC:
We demonstrate the unpleasant distillation performance guarantee of 0(1/(177²²) for PBC, and theoretically derive novel objective of Av-PBC that has much tighter performance guarantee of (011(111)))
Extensive experiments on multiple offline RL datasets verify significant improvements on OBD performance and speed by Av-PBC.
2 Related works
Offfine RL Data collection can be both hazardous (e.g. autonomous driving) and costly (e.g. healthcare) with the online learning paradigm of RL. To alleviate the online interaction, offline RL has been developed to learn the policy from pre-collected dataset gathered by sub-optimal behavior policies [Lange et al. 2012 Fu et al.] 2020). However, the offline paradigm limits exploration and results the distributional shift problem: (1) the state distribution discrepancy between learned policy and behavior policy at test time; and (2) only in-dataset state transitions are sampled when conducting
Bellman backup [Bellman| 1966) during the training period [Levine et al., 2020). Various offline RL
algorithms have been proposed to mitigate the distributional shift problem. Fujimoto and Gu [2021]. Tarasov et al.] [2024) introduce policy constrain that control the discrepancy between learned policy and behavior policy. To address the problem of optr-optiiistic estimation on out-of
actions, Kumar et al. (2020), Nakamoto et al. 2203), Kostrikov et al. 2022 propose to regularize the learned value function for conservative Q learning. Moreover, ensemble approaches have also proven effective in offline RL [An et al.) 202T]. Readers can refer to [Tarasov et al. [022) for a detailed
comparison of offline RL methods. Albeit these advancements, the offline dataset is extremely large

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(million-level) and contains sensitive information (e.g. medical history) [Qiao and Wang 2023]] necessitating consideration of training efficiency, data storage, and privacy concerns. To address these issues, we distill a small behavioural dataset from vast subpar offline RI. data to enable efficient policy learning via BC.
Given the resource constraints in era of big data, numerous approaches have focused on improving learning efficiency through memory-efficient model (Han et al. 2016 Jing
Dataset Distillation
et al. 2021] and effective data utilization [Mirzasoleiman et al. 2020 Jing et al.) 2023 Lei et al.
2023 Recently, dataset distillation (DD) has emerged promising technique for condensing large
real datasets into significantly smaller synthetic ones, such that models trained on these tiny synthetic datasets achieve comparable generalization performance to those trained on large original datasets [Sachdeva and McAuley 2023] Yu et al. 20244 [Lei and Tao 2024]. This approach addresses key issues such as training inefficiency. data storage limitations, and data privacy concerns. There are two primary frameworks for DD: the meta-learning framework, which formulates dataset distillation as bi-level optimization problem [Wang et al. 2018 Deng and Russakovsky. 2022]] and the matching framework, which matches the synthetic and real datasets in terms of gradient (Zhao et al. 2021
Zhao and Bilen| 2021], feature (Zhao and Bilen
2023
Wang et al. 2022 or training trajectory
Cazenavette et al. 2022 Cui et al.. [023]]
While most DD methods focus on image data, Lupu et al. 2024 propose behavior distillation (BD), extending DD to online RL regime. In (online) BD, small number of state-action pairs are synthesized for fast BC training by (1) directly computing policy returns through online interactions: and (2) estimating the meta- gradient w.t.t synthetic data via evolution strategies (ES) [Salimans et al. 2017]. We underline that our OBD is not an extension of online BD, but rather a novel and parallel field because of different objectives that incur distinct challenges: (1) online BD uses the ground truth objective, i.e., policy return, by sampling many long episodes from environments. As a result. backpropagating the meta-gradient of return w.s.f. synthetic data is extremely inefficient, and Lupu jtt al. 2024] tackle the challenge by estimating meta-gradien with the zero-order algorithm of ES; and (2) OBD objective solely relies on offline data instead of long episode sampling, therehy making meta- ceta-gradient backpropagation relatively efficient and feasible, and the primary obstacle for OBD lies in designing an appropriate objective that accurately reflects the policy performance.
3 Preliminaries
Reinforcement Learning The problem of reinforcement learning can be described as the Markov y, decision process (MDP) (8, T,,,y,rrr dd), where S is set of states E S, A is the set of actions a E A. (s'l a) denotes the transition probability function, r(s, a) is the reward function, y E (0 is the discount factor, and (s) is the initial state distribution (Sutton and Barto 2018 We assume that the reward function is bounded by Rmaxs i.e., r(s, a) È Ranax] for all (s, E S x A. The objective of RL is to learn policy T(als) that maximizes the long-
expected return J(x) = E, 120 >rr,] where ra- = r((s, ax) is the reward at t-step, and y usually is close to 1 to consider long-how horizhorizon rewards in the most RL tasks. We define d" (s) Pr(s, s; and p², (x, a) = Pr(*t 8, a; T as (-th step state distribution and state-action distribution, respectively. Then, the discounted stationary state distribution (s) = (11 7) Di=ordd (s), and the discounted stationary state-action distribution Pa (s. a) (1 - 7) Σt= 7 pL a). Intuitively, the state (state-action) distribution depicts the overall "frequency" of visiting a state (state-action) with π. The action-value function of is 9x (s, E, Et 7're Su = 8, ag a). which is the expected return starting from s, taking the action a. Since ri 2 O, we have (= a) 2 0 for all (s, a).
Instead of interacting with the environment, offline RL learns the policy from sub-optimal offline dataset Doft = {(s;, dg, si, r.)):Ntt with specially designed Bellman backup Levnee et al. 2020 Although Dott is normally collected by sub-optimal behavior policies, offline RL. algorithms can recapitulate a near-optimal policy n² and value function qu- from Dort-
Behavioral Cloning [Pomerleau] [991] can be regarded as special offline RL algorithm and only copes with high-quality data. Given the expert demonstrations Dac {(5,, a.)) the policy network тe parameterized by 0 is trained by cloning the behavior of the expert dataset Dec in supervised manner: ming (0, Dec) == E(s,a)>Doc (TO (a|s) # (als))² where 7 (als)) =
3

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Eing Ms [. is an empirical estimation based on DBc. Compared to general offline RL algorithms Σ Map [s;=s)
that deal with subpar 4-tuples of Dott. BC only handles expert 2-tuples, while has better convergence speed due to the supervised paradigm. This paper aims to distill massive sub-optimal 4-tuples into
few expert 2-tuples, thereby enabling rapid policy learning via BC.
3.1 Problem Setup
We first introduce behavior distillation (Lupu et al. 2024 that aims to synthesize few data points D Dey {s,, a;) N with small Naya from the environment, so the policy trained on Daya has a large expected return J. The problem of behavior distillation can be formalized as follows:
D sym
arg max J (TO(D)) s.t. 8(D) arg min (cc( D).
(1)
D
During behavior distillation, the return J is directly estimated by the interaction between policy and environment. However, in the offline setting, the environment can not be touched, and only the previously collected dataset Dorr is provided. Hence, we employ H(TTe, Dott) surrogate loss to estimate the policy performance of hTe given the offline data Dort without interactions with the environment. Then, by setting Naya < Note, offline behavior distillation be formulated as below:
D paya arg min H. (O((D).oott) s.t. ((D) arg min Cac (0, D).
3.2 Backpropagation through Time
The formulation of offline behavior distillation is a bi-level optimization problem: the inner loop optimizes the policy network parameters based on the synthetic dataset with BC by multiple iterations of {01, 82 ... 0r J During the outer loop iteration, synthetic data are updated by minimizing the surrogate loss H. With the nested loop, the synthetic dataset gradually converges to one of the optima. This bi-level optimization can be solved by backpropagation through time (BPTT) [Werbos] 1990
0H
ÖH.
A T
T0(T)
ag(k)
ag(T)
T
ag(0)
V DDH 0D 00(T)
=
00(k)
3D
and
200
II
000-1)
(3)
k
Although BPTT provides a feasible solution to compute the meta-gradient for OBD, the objective H hardly minimized to near zero in practice owing to the severe complexity and non-convexity of bi-level optimization [Wiesemann et al. 2013
4 Methods
The key challenge in OBD determining an appropriale objective loss H(TV, Doff) to estimate the performance of тT. While policy performance could be naturally estimated using episode return by learning MDP environment from Doer, as done model-based offline RL (Kidambi al., 2020). this approach is computationally expensive. Apart from the considerable time required to sample the episode for evaluation, the corresponding gradient computation also inefficient: although Policy Gradient Theorem ØJ du (s) La 4r (s. a) (a)o(()s) provides way compute meta- gradients [Sutton and Barto 2018). the gradient estimation often exhibits high variance due to the lack of information w.s.l. da and g (x(sa)
4.1 Data-based and Policy-based BC
Compared to both sampling and gradient computation inefficiency of policy return, directly using Dott is more feasible way to estimate the policy performance in OBD, and natural option is BC loss, i.e., H(TT. Dost) = (Bc(8 Does). which we refer to as data-based BC (DBC). However, as Dott is collected by sub-optimal policies, DBC hardly evaluates the policy performance accurately.
Benefiting from offline RL algorithms, we can extract the near-optimal policy x* and corresponding value function dx- from Dott via carefully designed Bellman updates. Consequently, a more rational choice to correct actions Dott with x², leading to H(T, Dott) Eep [Drv (Tr (-Is), (-1ss)),, where Drv (xr" s), ((- s)) E.Ed [|="" (a|s) TTaa [}] is the total variation (TV) distance

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that measures the decision difference between n" and π at state and we term this metric policy- based BC (PBC). With the exemplar x offline behavior distillation performance J(z), where is trained on Dayn: can be guaranteed by the following theorem.
Theorem 1 (Theorem 1 in [uu et al., 2020]). Given two policies of x and π with Bgwdd (+) (Drv (x (-1s), (-1s)) S,, we have J(x") J(x) (T-pse.
Remark 1. The proof of Theorem does not necessitate that nt is superior to n, and thus substituting do. (8) in (s)d).(s) (s) [Drv (T* (-|s), rT-|s)]] S with dx (s) does not alter the outcome.
Theorem D clucidates that æ has close performance to the good policy π as long as they act similarly, and (a) (x=)) if their decision difference Drv (T* (-) IT-- s)) O. This is optimistic for the conventional BC setting where the loss can be easily optimized to near zero. However, because of intractable bi-level optimization, the empirical objective is rarely decreased to small values in OBD. According to [Xu et al., 2020], the upper bound in Theorem i tight as quadratic discount
complexity (1 - -7)") is inevitable in the worst-case, implying that the distillation performance guarantee collapses quickly the PBC objective increases. To this end, more effective OBD objective should be considered to ensure stronger distillation guarantees.
4.2 Action-value weighted PBC
The preceding analysis highlights the inferior distillation guarantee of ((1((1 -)) with PBC. To establish a superior OBD objective, we prove the equivalence between the performance gap of ((T) and action-valle value weighted x² (als) - (a|s) (Theorem 2 By optimizing the weighted decision difference, the performance gap can be non-vacuously bounded with a reduced discount complexity of (1/((1 - -)) (Corollary 1]. Motivated by these theoretical insights, we propose action-value weighted PBC as the OBD objective for a tighter distillation performance guarantee.
Theorem 2. For any two policies π and x², we have
J(TT) - [(T) 1 1-y Bend, (8) [ax- (s, (-18) - π (+18))
(4)
where the dot notation (.) is a summation over the action space, ie., Iu (8, (n* (-18) (+18)
EaEA 9x- (8,a) (x" (als) - x (als)).
Proof Sketch. (1) With RL definitions, we represent J(TT' - [TT) by
J(T)) - [(T) Eg (s) [y.- (s, (TT (-1s) r-|1s)]] (p (1r- (8, on (8,
(2) then we prove the iterative formula w.nt (pp(s,a) (r (s, a) 9x (s,a)):
(pg(s.)) [g (s,a) 9n (s,a)]
=yB (s) [g (s, -) (T (+Is) 7 (-1ss)]] + + (0,0) Igx. (s, qu (s)
(3) integrating the two equations above yields the desired result
J(m²) J(TT) J(x)
7" Tendd (e) la (s, (I (-18) 1000-((115) (-(s))]
The complete proof can be found in Appendix A.1 Since 4r- (s.a) represents the expected return under the decent policy nt when staring from (s, a) and reaches the maximum if is truly optimal, it can be interpreted as the importance of (s, a), and higher return is likely to be achieved when starting from more important (s, a). Consequently, the gap between Jxx*) and J(x) directly depends on the importance-weigien
decision difference between π and æ. Based on Theorem 2 and Jx 2 O. we can readily derive a bound on the guarantee on [J(T*) J(T) by applying the triangle inequality.
Corollary 1. Given two policies of nr and π with Egnd=(s) (s) I (8,-) | (-1s) T (-1s))] < we have [J(x*) J(x) S
Tightness Since only the triangle inequality is applied, there exists the worst case for where T" (ajs) T(ass) < 0 holds only when gx- (8, a) = This makes the inequality collapse to equality
in Corollary [ thereby demonstrating that the upper bound in Corollary [ is non-vacuous.
5

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Algorithm 1: Action-value weighted PBC
Input :offline RI dataset Dote, synthetic data size Nayn: loop step T, Tout, learning rate on.
(r1, momentum rate 90. Sn
Output: dataset Daya
T² 0x + -ffflinenL(Dort
Initialize Dayn {8s a:)) a;)) by randomly sampling (se, az) Dott for Yout = to Tox do Randomly initialize policy network parameters 0g
> Behavioral cloning with synthetic data.
I do for =ort=1e 1
Compute the BC loss w.r.t. synthetic data Li-1 = (0c Daya) Update 8, GradDescent( Ct-1, Crp (b)
end
[8] by sampling 8; ~ Dorr and as ~ x² (-18s) Compute H( B) B E ax- (s), a;) (Ter (agls;) n=" (a:ls:))2
Construct the minibatch B = {88, a;) a=)
Update Dayn < GradDescent (V (VD., H(TTer B), on, 31)
end
Comparison to Thm.
With the fact qm- (s, S Ei Rmax
Rmax I-7
we have
Rmax
Egnd (e) [9 (s, | (-1s) * (-1s)]] - 1-7 (s) [|T (-1s) - x x(-[s)],,
(5)
therefore our bound in Corollary 1 is significantly tighter than Theorem I 9n- (s, = Riax requires n" to achieve the maximum reward at every step. This condition is particularly difficult for sparse-reward environments where most r(s, a) are close zero. Moreover, combining the proof of Theorem P and Eq. proviides a more straightforward proof of Theorem []
As shown by the theoretical analysis, action-value weighted objective offers stronger distillation guarantees due to the linear discount factor complexity ((1/(1-7) This improvement alleviates the loose guarantee caused by limited optimization in OBD compared to former quadratic (1)))) Accordingly, we propose action-value weighted PBC (Av-PBC) as the OBD objective:
H(T, Dots) = EowDes (a- (s. (s, (ir (-1s) - (-s)))
(6)
While Av-PBC theoretically induced, it quite intuitive to understand: states in Dorr are normally sampled by mixture of policies instead of the expert π². If we sampled a bad state s with extremely small ge (s, a), measuring the decision difference between и and x will be less important. As for practical implementation, Eq. requires summing over the entire action space A to compute E.E. which is highly inefficient for large [AA. Considering the expert policy is typically highly concentrated, ie., only few actions are selected by x" with large action values, we instead sample T" (+|8) ) to efficiently estimate Eq. 6. The pseudo-code of Av-PBC is presented in Algorithm
Experiments
In this section, we evaluate the proposed ODB algorithms across multiple offline RL datasets from perspectives of (1) distillation performance, (2) distillation convergence speed, (3) cross-architecture and cross-optimizer generalization, and (4) policy ensemble performance w.rl. distilled data.
Datasets We conduct offline behavior distillation on D4RL [Fu et al. 2020), widely used offline RL benchmark. Specifically, OBD algorithms are evaluated on three popular environments of Halfcheetah, Hopper, and Walker2D. For each environment, three offline RL datasets of varying quality are provided by D4RL, i.e., medium-repla (M-E) datasets. Thus, total of 3 3 9 datasets are employed to assess OBD algorithms. medium dataset is collected from the environment with "medium" level policies; medium-replas dataset consists of recording all samples in the replay buffer observed during training this "medium" level policy; and medi medium-en teiiimmeeeee ieeppeem-eperttt dataset is mixture of expert demonstrations and sub-optimal data.
(M-R), medium (M), and medium-exper expert

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Table 1: Offline behavior distillation performance on D4RL offline datasets. The result for Random Selection (Random) is obtained by repeating times. For DBC, PBC, and Av-PBC, the results are averaged across five seeds and the last five evaluation steps. The best OBD result for each dataset is marked with bold scores, and orange-colored scores denote instances where OBD outperforms BC.
Halicheetach M
Hopper M
Walker2D M
Method
Average
M-R
M-F
M-R
M-F
M-R
M-F
Random
0.9
1.8
2.0
19.1
19.2
11.6
1.9
4.9
7.6
DBC
28.2
29.0
12.1
37.8
31.1
29.3
11.7
20.9
PBC
19.4
30.9
20.5
35.6
25.1
33.4
41.5
33.2
34.0
30.4
Av-PBC
35.9
36.9
22.0
40.9
32.5
38.7
55.0
39.5
42.1
38.2
BC (Whole) 14.0
42.3
59.8
22.9
50.2
51.7
14.6
65.9
89.6
45.7
OfRL (Whole)
45.8
47.6
50.8
98.0
56.4
107.3
87.4
84.0
109.0
70.1
Setup The advanced offline RL algorithm of Cal-QL Nakamoto et al. 2023 is utilized to extract the decent T' and 9r* from Dose- four-layer MLP serves as the default architecture for policy networks. The size of synthetic data Neyn is set to 256. Standard SGD is employed in both inner and outer optimization, and learning rates Og 0.1 and 0n 0.1 for the inner and outer loop, respectively, and corresponding momentum rates 3n = 0 and B1 0.9. Additional implementation details are provided in Appendix
Evaluation
To accesss the performance of D Deyn. we train policy networks on Dayn with standard
BC, and obtain the corresponding averaged return by interacting with the environment for 10 episodes. We use normalized return Fu et al. 2020] for better visualization: normal ized return =
100 x expert return zandom return' where random return and expert return refer to returns of random policies and the expert policy (online SAC [Haarnoja et al. 2018)), ), respectively.
return randon return
Baselines (1) Random Selection: randomly selecting N real state-action pairs from Dorr (2) DBC: (3) PBC; (4) Av-PBC. We also report policy performance of behavioral cloning and Cal-QL in terms of training on the whole offline dataset Darr for comprehensive comparison.
5.1 Main Results
We first investigate the performance of various OBD algorithms (DBC, PBC, Av-PBC) across offline datasets of varying quality and environments, as detailed in Table Several observations are obtained from the results: (1) offline behavior distillation effectively synthesize informative data that enhance policy training (DBC/PBC/Av-PBC vs. Random Selection); (2) PBC demonstrates better distillation performance than the basic DBC, especially given the low-quality RL data, highlighting the benefit of action correction in the sub-optimal data (30.4 vs. 20.9): (3) Av-PBC considerably outperforms PBC across all datasets (38.2 vs. 30.4); (4) when the offline data are collected by low-quality policies (med im--lalay) Av-PBC can surpass BC trained on the whole data, while it gradually lags behind BC with higher-quality offline data (medium-reph) um-rella and medium mediun-expert); (5) given that the objective of OBD is to approximate the decent policy extracted by offline RL algorithms, offline RL serves as an upper bound for OBD performance. In summary, the empirical results show that Av-PBC increases OBD performance by substantial margin compared to the baselines (82.8% for DBC and 25.7% for PBC).
An interesting phenomenon observed with Av-PBC is that synthetic data distilled from medium-repl lay offline datasets exhibit better performance than those distilled from medium-eapers offline datasets. We explain here: while peddim--expen data offer better quality, medium-replay data contains more diverse states due to being sampled by a mixture of less-trained policies that explore wider rage of states. This is similar to
dilemma in RL SStton and Barto 2018 and underscores the importance of state coverage in original data for OBD.
Training Time Comparison To further illustrate the advantages of OBD, we compare the time required for training polices on original data versus OBD-distilled data. For synthetic data with a size of 256, only 100 optimization steps are necessary, corresponding to a training time of 0.2s, while 25k~115kk steps are required for BC on original data. With distilled data, the training time can be reduced by over 99.5%. A detailed list of training steps for all datasets is provided in Appendix C
7

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BC
DBC
PBC
Av-PBC
FA Toheetah medi Top Lay
Hopper medium- replay
Walker21 medi replay
25.
50c
125
289x
Step
Step
Holf ah modium
Hoppet medi
Kalke:2D medium
Normalyen Rettum
Noreel lallure
Stop
HalEcheete an ne meddiuu-eeee
Hopper med tum expert
Ma. 2D med1 Lum expert
Netronalion Hesture
Nomelred
289K
Step
(a) Halfcheetah
(b) Hopper
(c) Walker2D
Figure I: Plots of OBD performance, represented by the normalized returns of policies trained on synthetic data, functions of distillation steps on (a) Halfcheetah; (b) Hopper; and (c) Walker2D environment. Each curve averaged over five random seeds.
Table 2: Offline behavior distillation performance across various policy network architectures and optimizers (Optim). Red-colored scores and green-colored scores in brackets denote the performance degradation and improvement, respectively, compared to the default training setting. The results averaged over five random seeds and the last five evaluation steps.
Halfcheetach M
Hopper M
Walker2D
Arch/Opt
Average
M-R
M-E
M-R
M-E
M-R
M-E
Oplm Architecture
2-layer
37.1
35.9
10.9
29.9
26.2
33.9
49.2
41.3
51.1
35.1
3-layer
38.6
39.7
19.4
39.0
28.1
41.5
63.2
44.1
55.3
41.0
5-layer
36.1
37.7
20.0
37.1
29.1
36.6
52.0
36.7
31.6
35.2 (3.0)
6-layer
32.1
36.0
17.3
36.9
29.6
32.8
47.1
28.2
25.5
31.7 (6.5)
Residual
36.9
36.4
20.0
38.8
29.8
40.3
47.5
35.7
37.1
35.8
Adam
35.8
37.6
22.9
40.5
31.2
40.2
55.8
41.9
47.7
39.3 (1.1)
AdamW
36.8
37.9
21.4
40.6
33.3
41.1
55.4
44.2
43.2
39.3 (1.1)
SGDm
36.4
37.3
21.8
40.4
30.9
39.2
54.7
40.2
42.1
38.1 (0.1)
Convergence Speed of OBD To compare the convergence speed of OBD algorithms, we plot the performance of various OBD algorithms over distillation step; please see Figure [ These plots demonstrate that Av-PBC not only improves the OBD performance, but has significant convergence speed and requires only a quarter of the distillation steps compared to DBC and PBC, which is essential for OBD considering the compute- compute-intensie intensivee bi-level optimization.
Cross Architecture and Optimizer Performance We evaluate the synthetic data across various training configurations assess the cross-aree architecture/opiimizer generalization Av-PBC. Con- cretely, we employ the data distilled by Av-PBC with the default network (4-layer MLP) and optimizer (SGD) to train (1) different networks of 2/3/5/66-lyer and residual MIPs and (2) the default 4-layer ML.P with different optimizers of Adam, AdamW, and SGDm (SGD with momentum=0.9), The

---

Table 3: Offline behavior distillation performance on D4RL offline datasets with ensemble num of 10. Green-colored scores in brackets denote the performance improvement compared to the non-ensemble setting. The results are averaged over five random seeds and the last five evaluation steps.
Halfcheetach
Hopper M
Walker2D M
Method
Average
M-R
M
M-E
M-R
M-E
M-R
M-E
DBC
2.0
30.0
31.8
9.3
44.9
43.3
5.8
50.6
33.6
27.9 (7.0)
PBC
12.9
33.4
31.6
36.6
36.7
41.8
64.1
41.6
42.0
37.9 (7.3)
Av-PBC
39.8
41.4
37.2
39.7
27.6
38.8
75.9
58.6
73.7
48.1 (9.9)
results are presented in Table As shown in the last column of average performance, we observe that (1) albeit slight drop, synthetic data distilled by Av-PBC are still valid in training different policy networks, and (2) the performance of distilled data is relatively robust to the variation of optimizers. Therefore, the
data possess satisfied cross- catassccccitecturropmiiiii
performance.
Policy Ensemble on OBD Data With the tiny distilled dataset, policy ensemble can be efficiently performed further enhance policy performance. This is achieved by training multiple policy networks on synthetic data and then combining their outputs to generate actions. To evaluate the performance gain from policy ensemble, we train 10 policy networks with different seeds; please see Table The results demonstrate that (1) policies trained on synthetic data can be substantially boosted through ensemble (25.8% for Av-PBC); and (2) Av-PBC exhibits a larger performance gain than DBC and PBC (9.9 vs. 7.0/7.3), highlighting the advantages of Av-PBC in policy ensemble.
Discussion
Distilled behavioral data encapsulate critical decision-makin knowledge from offline RL data and associated environment, making them highly applicable to various downstream RL tasks. Through BC on distilled data, we can rapidly pretrain a good policy for online RL fine-tuning [Goecks et al., [211]]. On the other hand, after offline pretraining, the policy can be further enhanced by online fine-tuning, while there exists catastrophic forgetting w.ztt offline data knowledge during fine-tuning [Luo et al., 2023). To tackle this challenge, (Zhoo et al. [2022] propose to use BC loss w.t.t offline data constraint during the fine-tuning phase. By replacing the massive offline data with distilled data, we can achieve more efficient loss computation and thus better algorithm convergence. similar approach can be achieved to circumvent catastrophic forgetting in continual offline RL [Gai et al. 2023), where the goal is to learn sequence of offline RL tasks while retaining good performance across all tasks. Moreover, multi-task offtine RL (Yu et al. 202T], which learns multiple RL tasks jointly from a combination of specific offline datasets, also receives benefits from OBD in terms of efficiency by alternative training on the mixture of distilled data via BC (Lupu et al. 2024
Applications
Beyond benefits in efficient policy training, OBD shows potential for protecting data privacy: given that offlin datasets often contain sensitive information, such as medical records, privacy concerns significant offline RL due to various privacy attacks on the learned policies [Qiao and Wang 2023) OBD enhance privacy preservation by publishing smaller, distilled datasets instead of the full, sensitive data. Besides, distilled behavioral data is also beneficial for explainable RI. by highlighting the critical states and corresponding actions. A example of this is provided in Appendix D
Limitations The OBD data are 2-tuples of (state, action) and exclude reward. Thus, the distilled data are solely leveraged by the supervised BC and invalid for conventional RL algorithms with Bellman backup. Despite this deficiency, OBD data still facilitate the applications above by efficiently injecting high-quality decision-makinn making knowledge into policy networks with BC loss.
We note that two major challenges remain in current OBD algorithms: distillation inefficiency and policy performance degradation. While our Av-PBC substantially decreases the distillation steps, the OBD process is still computationally expensive (25 hours for 50k distillation steps on a single NVIDIA V100 GPU) due to the bi-level optimization involved. Moreover, there remains a notable performance gap between OBD and the whole data with offline RI algorithms (38.2 vs. 70.1 1 in Table [p. These limitations also shed light on future directions in improving the efficiency of OBD and bridging the gap between synthetic data and the original offline RL datasct.

---

7 Conclusion
In this paper we integrate the advanced dataset distillation with offline RL data, formalizing the concept of offlin behavior distillation (OBD). We introduce two OBD objectives: the naive offline data-based BC (DBC) and its policy-corrected variant, PBC. Through comprehensive theoretical analysis, we demonstrate that PBC offers inferior OBD performance guarantee of O(1/(1 - 7) under complex bi-level optimization, which inevitably incurs significant distillation loss.. To tackle this issue, we theoretically establish the equivalence between policy performance gap and action- value weighted decision difference, leading the proposal action-value weighted BC (Av-PBC). This novel Av-PBC objective significantly improves the performance guarantee (L1((1 ()) Extensive experiments on multiple offline RL datasets demonstrate that Av-PBC vastly enhances OBD performance and accelcrates the distillation process by several times.
Acknowledge
The authors thank the anonymous reviewers for their helpful comments and feedback. The authors are also grateful Zhihao Cheng for thoughtful discussions and fruitful comments. Dr Tao is partially supported by NTU RSR and Start Up Grants.
References
Gaon An, Seungyong Moon, Jang-Hyun Kim, and Hyun Oh Song. Uncertainty- based offline reinforcement learning with diversified q-ensemble. Advances in neural information processing systems, 34:7436-7447, 2021.
Richard Bellman. Dynamic programming. science, 153(3731):34 1966.
George Cazenavette, Tongzhou Wang, Antonio Torralba, Alexei A. Efros, and Yan Zhu. Dataset distillation by matching training trajectories. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2022.
Justin Cui, Ruochen Wang, Si Si, and Cho-Jui Hsieh. Scaling up dataset distillation imagenet- 1k with constant memory. In Proceedings of the International Conference on Machine Learning (ICMI.), 2023.
Zhiwei Deng and Olga Russakovsky. Remember the past: Distilling datasets into addressable memories for neural networks. In Alice H. Oh, Alekh Agarwal, Danielle Belgrave, and Kyunghyun Cho, editors, Advances in Neural Information Processing Systems, 2022. URL httpps://operrevie.. http://wweee//toomm////////. wwgfa.
Justin Fu, Aviral Kumar, Ofir Nachum, George Tucker, and Sergey Levine. D4rl: Datasets for deep data-driven reinforcement learning, 2020.
Scott Fujimoto and Shixiang Gu. A minimalist approach to offline reinforcement learning. In A. Beygelzimer, Y. Dauphin, P. Liang, and J. Wortman Vaughan, editors, Advances in Neural Infor- mation Processing Systems, 2021. URL htt/tt///////peerrr// wtt.:/oormmmmddd-333///oaaaam
Sibo Gai, Donglin Wang, and Li He. Offline experience replay for continual offline reinforcement learning. arXiv preprint 230. 2023.
Vinicius G Goecks, Gregory M Gremillion, Vernon J Lawhern, John Valasek, and Nicholas R Waytowich. Integrating behavior cloning and reinforcement learning for improved performance in dense and sparse reward environments. arXiv preprint arXiv: /et::0420000 2019.
Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor. In International conference on machine learming. pages 1861-1870. PMLR, 2018.
Song Han, Huizi Mao, and William J Dally. Deep compression: Compressing deep neural networks with pruning, trained quantization and huffman coding. International Conference on Learning Representations (ICLR), 2016.
10

---

Yongcheng Jing, Yiding Yang, Xinchao Wang, Mingli Song, and Dacheng Tao. aeta-aggre Learning aggregate for 1-bit graph neural networks. In ICCV, 2021.
Yongcheng Jing, Chongbin Yuan, Li Ju, Yiding Yang, Xinchao Wang, and Dacheng Tao. Deep graph reprogramming. In CVPR, 2023.
Rahul Kidambi, Aravind Rajeswaran, Praneeth Netrapalli, and Thorsten Joachims. Morel: Model- based offiine reinforcement learning. Advances neurul information processing systems, 33: 21810-21823, 2020.
Ilya Kostrikov, Ashvin Nair, and Sergey Levine. Offline reinforcement learning with implicit g-learning. In International Conference Learning Representations, 2022. URL https://
openreview. wttp:eteeeeooomomddddaaaaaaaaaa
Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine. Conservative q-learning for offline reinforcement learning. Advances Neural Information Processing Systems, 33:1 199-11991 2020.
Sascha Lange, Thomas Gabel, and Martin Riedmiller. Batch reinforcement learning. In Reinforcement learning: State-of-the-arl, pages 45-73. Springer, 2012.
Shiye Lei and Dacheng Tao. A comprehensive survey of dataset distillation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(01):17-32, jan 2024. ISSN 1939-3539, doi:
10.1100/PAAM222233.33222
Shiye Lei, Hao Chen, Sen Zhang, Bo Zhao, and Dacheng Tao. Image captions are natural prompts for text-to-image models. arXiv preprint arXiv:2307.060 200.:2307.00866. 2023.
Sergey Levine, Aviral Kumar, George Tucker, and Justin Fu. Offline reinforcement learning: Tutorial, review, and perspectives on open problems. arXiv preprint (xXiv:2005.0/643 2020.
Yicheng Luo, Jackie Kay, Edward Grefenstette, and Mare Peter Deisenroth. Finetuning from offline reinforcement learning: Challenges, trade-offs and practical solutions. arXiv preprint arXiv:2303.17396 2023.
Andrei Lupu, Chris Lu, Jarek Luca Liesen, Robert Tjarko Lange, and Jakob Nicolaus Foerster. Behaviour distillation. In The Twelfth International Conference Learning Representations, 2024. URL/ttps: / wtwp://wwwweeeeooomnieeeei.ee mett//frrrummiicequgrSrriii
Baharan Mirzasoleiman, Jeff Bilmes, and Jure Leskovec. Coresets for data-efficient training of machine learning models. In International Conference on Machine Learning, pages 6950-6960.
PMLR, 2020.
Mitsuhiko Nakamoto, Yuexiang Zhai, Anikait Singh, Max Sobol Mark, Yi Ma, Chelsea Finn, Aviral Kumar, and Sergey Levine. Cal-QL: Calibrated offline RL pre-training for efficient online fine- tuning. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL
Dean A Pomerleau. Efficient training of artificial neural networks for autonomous navigation. Neural computation, 3(1):88-97 97, 1991.
Dan Qiao and Yu-Xiang Wang. Offline reinforcement learning with differential privacy. In Thirty-seventh Conference on Neural Information Processing Systems, 2023. URL https
Noveen Sachdeva and Julian McAuley. Data distillation; A survey. Transactions on Machine Learning Research, 2023. ISSN 2835-8856. Survey Certification.
Tim Salimans, Jonathan Ho, Xi Chen, Szymon Sidor, and Ilya Sutskever. Evolution strategies as scalable alternative to reinforcement learning. arXiv preprint urXiv:/703.03864 2017.
Richard S Sutton and Andrew G Barto. Reinforcement learning: An introduction. MIT press, 2018.

---

Denis Tarasov, Alexander Nikulin, Dmitry Akimov, Vladislav Kurenkov, and Sergey Kolesnikov. CORL: Research-orienter deep offline reinforcement learning library. In 3rd Offline RL Workshop: Offline RI. as " "Launchpad"" 2022.
net/forum? BSy
Denis Tarasov, Vladislav Kurenkov, Alexander Nikulin, and Sergey Kolesnikov. Revisiting the minimalist approach to offline reinforcement learning. Advances in Neural Information Processing Systems, 36, 2024.
Kai Wang, Bo Zhao, Xiangyu Peng, Zheng Zhu, Shuo Yang, Shuo Wang, Guan Huang, Hakan Bilen, Xinchao Wang, and Yang You. Cafe: Learning to condense dataset by aligning features. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pages 12196-12205, 2022.
Tongzhou Wang, Jun- Yan Zhu, Antonio Torralba, and Alexei A Efros. Dataset distillation. arXiv preprint 1r1.v: 2018.
Paul Werbos. Backpropagation through time: what does and how do it. Proceedings of the IEEE, 78( 18510):550-1156, 1990.
Wolfram Wiesemann, Angelos Tsoukalas, bilevel optimization. SIAM Journal on Optimization, 23(1):353-380) 2013.
Kleniati, and Berç Rustem. Pessimistic
Tian Xu, Ziniu Li, and Yang Yu. Error bounds of imitating policies and environments. Advances in Neural Information Processing Systems, 13:15737-15749, 2020.
Ruonan Yu, Songhua Liu, and Xinchao Wang. Dataset distillation: comprehensive review. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(01):150-1700 jan 2024. ISSN 1939-3539. doi: 10. 1O../TTA...222...23..2..
Tianhe Yu, Aviral Kumar, Yevgen Chebotar, Karol Hausman, Sergey Levine, and Chelsea Finn. Conservative data sharing for multi-task offline reinforcement learning. Advances in Neural Information Processing Systems, 34:1 1501-11516, 2021.
Bo Zhao and Hakan Bilen. Dataset condensation with differentiable siamese augmentation. In International Conference Machine Learning, pages 12674 12685, PMLR, 2021.
Bo Zhao and Hakan Bilen. Dataset condensation with distribution matching. In Proceedings the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV), 2023.
Bo Zhao, Konda Reddy Mopuri, and Hakan Bilen. Dataset condensation with gradient matching. In International Conference on Learning Representations, 2021. URL httpps://ppeerreiieeee nnt// net/
forum? Dorun//id=SAAWLLIISSll
Yi Zhao, Rinu Boney, Alexander Ilin, Juho Kannala, and Joni Pajarinen. Adaptive behavior cloning regularization for stable offline-tor offline-to-onling online reinforcement learning. arXiv preprint arXiv:2210. 13846, 2022.
12

---

A Proofs
A.1 Proof of Theorem
Proof. With the definitions (s) [(als)d"- (s) and J(T) = (x)( l0x (s, we have
J(m") - ((T))
(s,aa In (s, (s, Ma (s,a)
Σ
[ (s, - a) (s.a)]
p
(s,0)ESAA
Σ
(m'(assdd (s, ((as) (s)
(s. a)
(x,0)ESAA
Σ (a|a) (3) (8, =als)) (5) (8,
(a,0)ESAA
+ (5) (s, (s (aals) (5) [s. = (s) = ds())
Egndd (s)
Σ
(#1(a))- x(ass)) (s,a) (p(() lo (8, du (s. (7)
LaEd
For the term Ox- (s, a) On (s, have
4= (s,a) 9x (s.a)
a)) + +-Bu
Σ
x (d'ls')) (sss))arr (s'
N'EA
ar(s,a) - -TBB)T((H(ea
a(a''s')
La'Ed
n' T''''s'') ( (d)
(8)
La'EA
Furthermore, due
we have
(sy(s,a) Ig.. (s, - In as)
=7
EXNT(("
Σ
r" (d'ls))) (5, - =(ddls)) (d',
L''A
=yB snB
Σ n (a)s)gmm (s,a) - (als)am (4.00)
aEd
n" (a (a))))ga (8, [r (s, + [(als)grr (8, =(als)a (5,0)
=>B
(a|s) T(als)) ax- (s, a)
+ + +rE
<(als)a Σ ( (s.
(8,
aad
LaEd
=7T5g-d-- (0)
(Ir (a|s) T(als)) a= (8,
+ yi, ( (0 (8, dx (8,a)]
(9)
aed
13

---

Plugging the iterative formula of Eq. 9 into Eq. 7 yields the desired equality:
J( - (Tr
E Egndy (0)
Σ
(als) - =(als)) 9m (8,a)
+ Epp(s.a) 1a (8, 9r (s, a)l
LaEd
"Bsnd
Σ
(T (als) - <[als)) -=- (s,a)
1=0
LEA
1
Bond= (a)
Σ
(mT T(als)) --- (s,
(10)
The last equation uses the definition that d=(s) (1 (1-7) Ei= ('d, The proof is completed.
L
B Implementation Details
This section provides all the additional implementation details of our experiments.
OBD Settings The policy network is 4-layer multilayer perceptron (MLP) with a width of 256. The synthetic data initialized by randomly selecting Nays state-action pairs from the offline data. For DBC and PBC, the distillation step Tout is set to 200k for Half cheetah and Walker2D and 50k for Hopper, respectively. For Av-PBC. the distillation step Tout Walker2D and 20k for Hopper. respectively. The inner loop step Tia is set to 100.
to 50k for Half cheetah and
Offline RL Policy Training We use the advanced offline RL algorithm of Cal-QL [Nakamoto et al. 2023 to extract the decent policy x² and corresponding value function dr from sub-optimal offline data, and the implementation in [arasovv al. 2022] employed our experiments with default hyper- parameter setting.
Cross-architecture Experiments. The width MLPs are both 256. The residual MLP a 4- MLP, and the intermediate layers are packaged into the residual block.
C Training Time Comparison
Table 4: The size and required training steps for convergence for each offline dataset. M denotes the million for simplicity. The size and step for synthetic data (Synset) are listed in the last column.
Halfcheetach
Hopper M
Walker2D M
Synset
M-R
M
M-E
M-R
M-E
M-R
M-E
Size
0.2M
1M
2M
0.4M
1M
2M
0.3M
1M
2M
256
Step (k)
40
25
100
80
50
100
60
50
125
0.1
For the whole original data, offline RL algorithms require dozens of hours. Therefore, we solely compare the training time of BC on synthetic data and BC on original data. Because the training time varies with GPU models (NVIDIA V100 used in our experiments), we report the optimization step, which has a linear relationship to training time, required for training convergence for each original dataset, as shown in Table
14

---

D Examples of Distilled Data
We present several examples of distilled behavioral data for Halfcheetah in Figure 2 The top row illustrates the distilled states, while the bottom row depicts the subsequent states after executing the corresponding distilled actions within the environment. The figure demonstrates that (1) the distilled states prioritize "critical states" or "imbalanced states" (for the cheetah) more than "balanced states"; and (2) the states following execution distilled actions are closer to "balanced states" compared to the initial distilled states. These examples offer insights into the explainability of reinforcement learning processes.
Detilled
Ned
Figure 2: Examples of distilled behavioral data. The top row shows the distilled states, while the bottom row presents the subsequent state following the execution the corresponding distilled actions within the environment.
E
The Performance of Av-PBC across Different Synthetic Data Sizes
We investigate the impact of varying synthetic data size OBD performance. The results, as shown in [5 suggest that OBD performance improves with an increase in synthetic data size. This enhancement is attributed to the larger synthetic datasets conveying regarding the RI. environment and associated decision-making processes.
comprehensive information
Table 5: The Av-PBC performance on D4RL offline datasets with different synthetic data sizes.
Synthetic Data Size
Dataset
16
32
64
128
256
Halfcheetah M-R
6.9
15.3
23.8
33.2
35.9
Hopper M-R
27.3
29.9
32.3
38.1
40.9
Walker2D M-R
14.8
21.8
34.0
50.0
55.0
15

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Reviews:
[{"review_id": "a2ZNXVBt7b", "reviewer": "Reviewer_rzRx", "summary": "This paper formulates offline behavior distillation in order to enable fast policy learning using limited expert data and thereby leveraging suboptimal RL data. The authors run extensive experiments on D4RL benchmarks to support their findings.", "questions": "I'd like the authors to add their thoughts on how the proposed methods can serve as building blocks towards resolving the limitations mentioned in the paper.", "limitations": "There are no significant technical limitations of this paper.", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. The linear discount complexity is a vast improvement over the prior quadratic discount complexity. \n2. Problem setup and assumptions are written nicely and proof sketches are succinct and concise.\n3. The application setting at the end of the paper, sheds light on the scope of the paper.", "weaknesses": "There are no major weaknesses, but ablation studies and further corollaries would strengthen the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1:** *There are no major weaknesses, but ablation studies and further corollaries would strengthen the paper.*\n\n**A1:** thanks for your acknowledgement and suggestion. We have conducted additional empirical studies during the response period to strengthen our paper: \n\n1. We explored the effect of different sizes of synthetic datasets on OBD performance. The results, presented in Table 2 of the PDF file, indicate that as the size of the synthetic data increases, OBD performance improves. This enhancement is attributed to the larger synthetic datasets conveying more comprehensive information about the RL environment and decision-making processes.\n2. We examined the role of state coverage in offline RL datasets $\\mathcal{D}_\\text{off}$ in enhancing OBD. Our empirical findings demonstrate that greater state coverage increases robustness against data noise, which is beneficial for OBD. For a detailed explanation, please refer to A2 in the global response.\n3. We provided illustrative examples of distilled Halfcheetah behavioral data in Figure 1 of the PDF file. The top row displays the distilled states, while the bottom row shows the subsequent states after executing the corresponding distilled actions in the environment. The figure reveals that (1) the distilled states emphasize \"critical states\" or \"imbalanced states\" (for the cheetah) more than \"balanced states\"; and (2) the subsequent states after taking distilled actions are closer to \"balanced states\" than the initial distilled states. These examples offer insights into the explainability of reinforcement learning processes.\n\n\n&nbsp;\n\n**Q2:** *I'd like the authors to add their thoughts on how the proposed methods can serve as building blocks towards resolving the limitations mentioned in the paper.*\n\n**A2:** Thanks for your suggestion. In our paper, we highlighted two primary limitations.\n1. The first limitation involves synthesizing distilled data for reinforcement learning. Our proposed Av-PBC partially addresses this issue by **distilling high-informative behavioral data for imitation learning, one of the offline RL methods**. This approach helps in effectively capturing essential information of the behavioral data, making it a valuable step towards resolving this limitation.\n2. The second major limitation concerns the high computational resources required for Offline Behavioral Distillation (OBD) due to the bi-level optimization process. Av-PBC offers a significant improvement in this area by enhancing the distillation speed. Specifically, it **reduces the required time to one-quarter** of what is needed by the naive OBD methods like DBC and PBC. This efficiency gain makes Av-PBC a practical and resource-efficient option. \nWe will provide a more detailed discussion in the revised version of the paper.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "522pKkZxnM", "reviewer": "Reviewer_kzVy", "summary": "The paper introduces Offline Behavior Distillation (OBD), a method to synthesize expert behavioral data from sub-optimal reinforcement learning (RL) data to enable rapid policy learning. The authors propose two naive OBD objectives, Data-Based Cloning (DBC) and Policy-Based Cloning (PBC), and introduce a new objective, Action-Value Weighted PBC (Av-PBC). Av-PBC optimizes the weighted decision difference to achieve superior distillation guarantees with linear discount complexity. Theoretical analyses and extensive experiments on multiple D4RL datasets demonstrate that Av-PBC significantly improves OBD performance and convergence speed when compared to the two navie OBD objectives. The paper further shows that the performance of Av-PBC generalize well across architectures of the policy network and optimizers.", "questions": "1. The \"Problem Setup\" is not straightforward without reading the following sections.\n\n     * 1.1.  Meaning of Capital D in Equation 1: In Equation 1, what does the capital D refer to? After reading the subsection \"Problem Setup\", it seems it might refer to the set of all trajectories in the environment. Could the authors clarify this?\n\n     * 1.2   Semantics of Surrogate Loss H(pi_theta, D_off):  The surrogate loss is initially introduced here for converting Equation 1 to Equation 2. While the missing clear definition of the surrogate loss makes it difficult to understand that minimizing H(pi_theta, D_off) is equivalent to maximizing the expected return J.  Referring to its definition in the \"Problem Setup\" would make the paper more readable. \n\n2. Algorithm 1 needs more clarification:\n\n    * 2.1.  Clarification on D_syn in Algorithm 1: In Algorithm 1, should \"D_syn\" be \"B\" in the step \"Compute H(πθT ,Dsyn)\" since the expression on the right side only involves data points from the sampled batch B?\n\n    * 2.2.  Use of GradDescent() in Algorithm 1: Algorithm 1 uses GradDescent() to update the synthesized dataset D_syn. This is understandable for updating policy parameters during behavior cloning, but could the authors clarify the semantics of applying GradDescent() to update D_syn?\n\n\n3. Examples of Discovered Critical States by Av-PBC: It is mentioned that \"distilled behavioral data is also beneficial for explainable RL by showing the critical states and corresponding actions.\" So, it will make the paper more convincing if some examples of such critical states discovered by Av-PBC could be added to the paper.", "limitations": "The authors have addressed some limitations of their work, such as the computational complexity of the bi-level optimization and the performance gap between the synthetic data and the whole offline RL dataset. However, they could further discuss potential limitations of the proposed approach in the following directions:\n\n1.   Generalization to Other Environments: While Av-PBC shows significant improvements on the D4RL benchmark datasets, its performance on more complex and diverse environments like Franka Kitchen and Adroit Manipulation remains unexplored. Future work could investigate the applicability and effectiveness of Av-PBC in these and other challenging environments to understand its generalization capabilities better.\n\n2.   Quality Requirement of Initial Offline Dataset: The paper discusses the performance of Av-PBC under three different qualities of datasets from three Mujoco environments. However, the quality of a dataset can vary widely in practice, potentially leading to failures of Av-PBC in certain scenarios. A discussion on the impact of dataset quality on Av-PBC's performance and practical guidance on applying Av-PBC across different scenarios would enhance its usability and robustness.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1. Originality: The paper introduces a novel approach to distill vast sub-optimal RL data into a limited set of expert behavioral data, enhancing policy training efficiency. The formulation of Av-PBC as an OBD objective is innovative and addresses the limitations of the two navie OBD objectives.\n\n2. Quality: The theoretical analysis is robust, providing a solid foundation for the proposed Av-PBC objective. The empirical results are comprehensive, covering multiple datasets and demonstrating significant improvements in OBD performance and efficiency.\n\n3. Clarity:  Overall, the paper is well-organized, with clear explanations of the problem setup, the proposed approach, and results. The theoretical proofs and empirical evaluations are detailed and easy to follow.\n\n4. Significance: The proposed method has broad implications for RL, enabling efficiency pretraining, data privacy protection and prior knowledge construction for downstream tasks.", "weaknesses": "1. The dependency on an offline RL algorithm makes the Algorithm 1 fails to claim that OBD could improve training efficiency when compared to direct application of the offline RL with the whole dataset since the training cost of an offline RL is part of the proposed Algorithm 1. Algorithm 1 requires that the an offline RL algorithm should learn pi* and q_{pi*} as an oracle before offline behavior distillation\n\n2. The result has limited discussion on the impact of the quality of the initial dataset on the effectiveness of the Av-PBC objective, limiting its applicability in practice. Adding more insightful discussion and possible guidance for when the Av-PBC could guarantee a performce could promote the adoption of the Av-PBC in practice. For example, an user may ask if it is worth to apply Av-PBC when given a pre-collected dataset. \n\n    * 2.1 Effectiveness Controlled by Dataset Quality: According to Table 1, the quality of the dataset D_off seems to control the effectiveness of the proposed approach. The approach only performs better than BC (whole) on the lowest-quality dataset (M-R). Can the authors discuss this finding in more detail?\n\n    * 2.2 Performance Patterns in Offline Datasets: The explanation for the \"interesting phenomenon for Av-PBC\" suggests that offline datasets with better state coverage lead to better OBD performance. However, the performance of Medium-Replay and Medium datasets from the HalfCheetah environment contradicts this. Based on their definitions, the M-R dataset has higher state-action coverage than the M dataset, but Av-PBC with the M dataset performs better. It might be worth to discuss these potential OBD performance patterns across offline datasets of different qualities by considering state-action coverage and average trajectory return collectively.\n\n    * 2.3 Av-PBC Ensemble Performance in Hopper Environment: The Av-PBC based ensemble does not improve OBD performance with the M-R and M datasets of the Hopper environment. It makes the paper stronger if the authors provide an explanation to guide potential users in applying the Av-PBC ensemble effectively.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1:** *The dependency on an offline RL algorithm makes Algorithm 1 fails to claim that OBD could improve training efficiency when compared to direct application of the offline RL with the whole dataset.*\n\n**A1:** Thanks for your comments. Though Algorithm 1 incorporates a complete offline RL process, once the distillation is complete, the distilled data can be reused in various scenarios. **This allows us to train policy networks much more efficiently on distilled data compared to using the large original dataset**. Improving the efficiency of OBD is a key focus for future work, particularly given the challenges of bi-level optimization, as discussed in Limitation. Notably, Algorithm 1 significantly enhances distillation speed compared to naive OBD methods such as DBC and PBC.\n\n&nbsp;\n\n**Q2:** *The result has limited discussion on the impact of the quality of the initial dataset on the effectiveness of the Av-PBC objective, limiting its applicability in practice.*\n\n**A2:** Thanks. Please refer to A2 in the global response.\n\n&nbsp;\n\n**Q2.1:** *The quality of the dataset $D\\_\\text{off}$ seems to control the effectiveness of the proposed approach in Table 1. The approach only performs better than BC (whole) on the lowest-quality dataset (M-R). Can the authors discuss this finding in more detail?*\n\n**A2.1:** Thanks for your observation. The quality of offline RL data $D\\_\\text{off}$ directly **affects the expert policy $\\pi^\\ast$ learned through offline RL algorithm**, thereby impacting the final performance of Av-PBC by the loss in Eq. 7. On the other hand, the policy $\\pi$ trained on distilled data typically performs below of $\\pi^\\ast$ due to optimization errors. **When original data is of lower quality, such as when sampled from sub-optimal or random policy (like M-R), the offline RL algorithm (Offline RL, whole) can learn a much better policy $\\pi^\\ast$ than BC (whole) because of its specially designed Bellman backup.** This significant performance gap between offRL (whole) and BC (whole) explains why our OBD algorithm performs better than BC (whole) with low-quality $D\\_\\text{off}$.\n\n&nbsp;\n\n**Q2.2:** *The \"interesting phenomenon for Av-PBC\" suggests that offline datasets with better state coverage lead to better OBD performance. Therefore, the Medium-Replay (M-R) dataset should have higher state-action coverage than the M dataset, but Av-PBC with the M dataset performs better.*\n\n**A2.2:** Thanks for your comments. We respectfully argue that we only claim that state coverage is crucial for OBD performance, and data quality is also another essential factor, as discussed in A2.1. Although M-R datasets have better state coverage, M datasets have superior data quality, which contributes to its better performance in the Halfcheetah environment. Our additional experiments further explore the impact of state coverage on OBD, revealing that greater state coverage enhances robustness against data noise, which benefits OBD performance. Please refer to A2 in the global response for more details.\n\n&nbsp;\n\n**Q2.3:** *Why does the Av-PBC based ensemble not improve OBD performance with the M-R and M datasets of the Hopper environment?*\n\n**A2.3:** Thanks for pointing this out. The reason the Av-PBC based ensemble does not improve OBD performance with the M-R and M datasets in the Hopper environment is that Hopper is simpler compared to Halfcheetah and Walker2D. Specifically, Hopper has a state dimension of 11 and an action dimension of 3, while Halfcheetah and Walker2D have state dimensions of 17 and action dimensions of 6. In more complex or high-dimensional environments, there is greater policy or model uncertainty, and policy ensembles are more effective at reducing this uncertainty and improving performance. In contrast, the simpler Hopper environment shows fewer improvements with the ensemble approach.\n\n&nbsp;\n\n**Q3:** *What does the capital $D$ in Eq. 1 refer to?*\n\n**A3:** Thanks. The capital $D$ refers to distilled data $D\\_\\text{syn}$.\n\n&nbsp;\n\n**Q4:** *Missing clear definition of the surrogate loss $H$ makes it difficult to understand that minimizing $H$ is equivalent to maximizing the expected return $J$ in Eq. 1 and Eq. 2.*\n\n**A4:** Thanks for your suggestion. We use the surrogate loss $H$ to approximate the expected return $J$. When $H$ is an appropriate proxy, minimizing $H$ effectively corresponds to maximizing $J$. We will clarify this in the revised paper.\n\n&nbsp;\n\n**Q5:** *In Algorithm 1, \"$D_{syn}$\" should be \"$B$\" in \"Compute $H(\\pi ,D_{syn})$\"*\n\n**A5:** Thanks and addressed.\n\n&nbsp;\n\n**Q6:** *In Algorithm 1, could the authors clarify the semantics of applying $\\texttt{GradDescent()}$ to update ${D}_\\text{syn}$?*\n\n**A6:** Thanks. In the first step of $\\texttt{GradDescent}$, we compute the meta-gradient $\\nabla_{D_\\textbf{syn}}$ via BPTT as shown in Eq. 3. Then we update $D_\\text{syn}$ by $D_\\text{syn} \\rightarrow D_\\text{syn} - \\alpha \\nabla_{D_\\text{syn}} $.\n\n&nbsp;\n\n**Q7:** *It will make the paper more convincing if some examples of such critical states discovered by Av-PBC could be added to the paper.*\n\n**A7:** Thanks for your suggestion. Please refer to A1 in the global response.\n\n&nbsp;\n\n**Q8:** *Generalization to Other Environments for proposed Av-PBC*\n\n**A8:** Thanks. We have tested our approach in three widely-used environments of Halfcheetah, Hopper, and Walker2D with various data qualities. Our experiments show that our Av-PBC consistently and remarkably improves the OBD performance compared to other methods in these nine datasets. We will generalize our Av-PBC to more environments in future work to further validate its effectiveness.\n\n&nbsp;\n\n**Q9:** *A discussion on the impact of dataset quality on Av-PBC's performance and practical guidance on applying Av-PBC across different scenarios would enhance its usability and robustness.*\n\n**A9:** Thanks. We provide additional insights on the impact of data quality and state coverage; please refer to A2 in the global response.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "kAOAffv9fS", "reviewer": "Reviewer_VAdy", "summary": "The paper considers the offline behavior distillation (OBD) for reinforcement learning. The problem is to distill a synthetic dataset given a large dataset sampled by a sub-optimal policy.  The key challenge of the problem is to design a good distillation objective. The authors first give two native objectives and prove they are limited to provide good performance guarantee. Then, they propose the Action-value weighted PBC objective and prove a better performance guarantee than the naive objectives. The authors evaluate the proposed algorithms on the dataset D4RL and demonstrate the distillation performance and show the advantage of OBD in reducing the RL training time.", "questions": "See the weakness section.  Also, I have the following comments.\n\n1. It is also a challenge to decide the size of the synthetic dataset to strike a balance between training efficiency and performance.\n2. I am also  concerned about the scaling issue. If the synthetic dataset  is large, the dataset distillation has a high computational cost.", "limitations": "The authors adequately addressed the limitations.", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The OBD problem is well motivated and closely related to the concerns of the community.", "weaknesses": "- Corollary 1 and Corollary 2 compare the policy for dataset distillation to the policy of offline RL, but we are more concerned about the performance of any policy trained on the distilled dataset comparing to the optimal policy. It would be better to propose a new metric to evaluate the performance of OBD for RL.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1:** *Corollary 1 and Corollary 2 compare the policy for dataset distillation to the policy of offline RL, but we are more concerned about the performance of any policy trained on the distilled dataset comparing to the optimal policy. It would be better to propose a new metric to evaluate the performance of OBD for RL.*\n\n**A1:** Thanks for your comments. As there is no assumption w.r.t. policies, we would like to clarify that in Corollaries 1 and 2, the policy $\\pi^\\ast$ can represent either a decent policy learned from an offline RL algorithm or the optimal policy. Since the environment and optimal policy are not accessible in the offline setting, we use advanced offline RL algorithms to derive an \"estimated expert policy\" $\\pi^\\ast$ from the offline RL data for the loss computation of OBD. Corollaries 1 and 2 theoretically show that this approach effectively assesses the performance of policies trained on the distilled dataset in relation to the practical benchmark policy $\\pi^\\ast$, given the constraints of the offline RL scenario.\n\n&nbsp;\n\n\n**Q2:**  *It is also a challenge to decide the size of the synthetic dataset to strike a balance between training efficiency and performance.*\n\n**A2:** Thanks for your comments. We have tested various sizes of synthetic datasets, and the results are presented in Table 1 of the PDF. This table demonstrates that OBD performance improves with larger synthetic datasets, as they provide more comprehensive RL environment and decision information during the OBD process.\n\nHowever, a larger synthetic dataset also presents challenges: (1) it increases the number of parameters in the bi-level optimization process, raising computational costs; and (2) it can reduce efficiency when training policies on the synthetic data. Determining the optimal size of the synthetic dataset depends on the specific RL environment and the coverage and quality of the pre-collected data. We plan to conduct a more detailed analysis on this topic in future work.\n\n&nbsp;\n\n**Q3:** *Scaling issue: if the synthetic dataset is large, the dataset distillation has a high computational cost.*\n\n**A3:** Thank you for bringing this up. While there is a trade-off between performance and efficiency related to the synthetic data size in OBD (see A2 above), OBD is primarily intended to distill a compact synthetic behavioral dataset for efficient policy training. As the synthetic dataset grows larger, the benefits of OBD diminish. Consequently, we focus on optimizing OBD performance within a limited synthetic data budget. We will incorporate this discussion into our revised manuscript.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "t1RKeW1GBI", "reviewer": "Reviewer_2J9f", "summary": "This paper emphasizes on the offline data generation to enable rapid policy learning in reinforcement learning. A new surrogate loss function is proposed for the data generation. Theoretical analysis shows the superiority of the proposed method in the performance gap.", "questions": "Please refer to Weakness.", "limitations": "N/A", "rating": 5, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 2, "strengths": "1. A new objective for data generation is proposed with a performance guarantee.\n2. Experiments are conducted over multiple benchmark datasets.", "weaknesses": "1. Related work on offline data generation of RL should be provided and compared. The proposed Av-PBC method is only compared with random policy, are there other related works? Is this paper the first work of offline data generation in RL?\n2. In section 1, it is not clear what is the difference between AvPBC and Av-PBC. Only Av-PBC is evaluated in the experiments.\n3. The network architecture is not clear. Since data generation is required. A generating network should be used in addition to a policy network. More details about the data generation model should be provided.\n4. In the experiments, what is the number of offline datasets as the number of offline data samples influences performance?\n5. In the experiments, the time and performance of Av-PBC and OffRL should be compared under varying numbers of generated data.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Q1:** *Related work on offline data generation of RL should be provided and compared. The proposed Av-PBC method is only compared with random policy, are there other related works? Is this paper the first work of offline data generation in RL?*\n\n**A1:** Thanks for your comments. To the best of our knowledge, our paper is the first to achieve behavioral data distillation from offline RL data.  We introduced the novel OBD algorithm Av-PBC and demonstrated its effectiveness by comparing it with two baseline methods, DBC and PBC. Our method shows significant improvements in both performance and speed across multiple datasets.\n\nThe most closely related work to ours is (online) behavioral distillation [1]. We have detailed the differences between [1] and our work in the Related Works section (Line 103-114). Our focus is on the offline scenario, where the RL environment is not accessible. This distinction is crucial as it highlights the unique challenges and contributions of our approach; please refer to Line 103-114 for more details.\n\n&nbsp;\n\n[1] Andrei Lupu, Chris Lu, Jarek Luca Liesen, Robert Tjarko Lange, and Jakob Nicolaus Foerster. Behaviour distillation. In *The Twelfth International Conference on Learning Representations*, 2024.\n\n\n&nbsp;\n\n\n**Q2:** *It is not clear what is the difference between AvPBC and Av-PBC in Section 1.*\n\n**A2:** Thanks and addressed. \"AvPBC\" is \"Av-PBC\" in Section 1.\n\n&nbsp;\n\n**Q3:** *The network architecture is not clear. Since data generation is required. A generating network should be used in addition to a policy network. More details about the data generation model should be provided.*\n\n**A3:** Thanks for your suggestion. We would like to clarify that our OBD method does not involve the use of generative models. Instead, we optimize the distilled data through backpropagation, applying an element-wise update as outlined by the $\\texttt{GradDescent}$ procedure in Algorithm 1. \n\n\nIn the first step of $\\texttt{GradDescent}$, we calculate the meta-gradient $\\nabla_\\mathcal{D_\\textbf{syn}}$ via Backpropagation Through Time (BPTT) as described in Equation 3. We then update $\\mathcal{D_\\textbf{syn}}$ by $\\mathcal{D_\\textbf{syn}} \\rightarrow \\mathcal{D_\\textbf{syn}} - \\alpha \\nabla_\\mathcal{D_\\textbf{syn}} $. We will provide additional clarification and detail about this process in our revised paper.\n\n&nbsp;\n\n**Q4:** *What is the number of offline datasets as the number of offline data samples influences performance?*\n\n**A4:** Thank you for your comments. We list the sample size of each offline dataset in Table 3 of the PDF file, which can also be found in Table 4 of the Appendix. These datasets range from 0.3 million to 2 million samples. Our Av-PBC significantly outperforms other approaches across these varying dataset sizes, demonstrating its robustness and effectiveness.\n\n&nbsp;\n\n**Q5:** *The time and performance of Av-PBC and OffRL should be compared under varying numbers of generated data.*\n\n**A5:** Thanks for your suggestion. We explored the effect of different sizes of synthetic datasets on OBD performance during the response period. The results, presented in Table 2 of the PDF file, indicate that as the size of the synthetic data increases, OBD performance improves. This enhancement is attributed to the larger synthetic datasets conveying more comprehensive information about the RL environment and decision-making processes.", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:
We appreciate all the reviewers for their enormous efforts and constructive comments. We will make sure to incorporate the parts that you suggested for clarity and reflect your feedback on the revised paper. We have compiled the results of additional experiments related to the reviewers' questions and comments in the attached PDF. The main contents of the file are listed as follows: 
- Figure 1: Examples of distilled behavioral data.
- Table 1: Behavioral cloning performance on the offline data **with varying levels of action noise**.
- Table 2: The Av-PBC performance on offline datasets **with different synthetic data sizes**.
- Table 3: Sample size for each offline dataset.

&nbsp;

The following responses present the reviewers' questions and corresponding details of experiments.


**Q1 (by Reviewer kzVy):** *It will make the paper more convincing if some examples of such critical states discovered by Av-PBC could be added to the paper.*

**A1:** Thanks for your suggestion. We have presented some examples of distilled Halfcheetah behavioral data in Figure 1 of the PDF file. The top row displays the distilled states, while the bottom row shows the subsequent states after executing the corresponding distilled actions in the environment. The figure reveals that (1) the distilled states emphasize "critical states" or "imbalanced states" (for the cheetah) more than "balanced states"; and (2) the subsequent states after taking distilled actions are closer to "balanced states" than the initial distilled states. These examples offer insights into the explainability of reinforcement learning processes. We will incorporate this into the revised paper.



&nbsp;

**Q2 (by Reviewer kzVy):**  *The result has limited discussion on the impact of the quality of the initial dataset on the effectiveness of the Av-PBC objective, limiting its applicability in practice.*

**A2:** Thank you for highlighting this point. We have addressed the impact of the quality of original offline RL data  $\\mathcal{D}\_\texttt{off}$ on OBD performance in Sec. 5.1 (Line 277-282), emphasizing the importance of state coverage of $\mathcal{D}_\text{off}$. **The OBD performance is influenced by both state coverage and quality of $\\mathcal{D}\_\texttt{off}$**. Below, we provide additional insights about these two factors:
1.  **Data Quality:** High-quality $\\mathcal{D}\_\texttt{off}$, which includes trajectories with high returns, enhances OBD performance by enabling the learning of an effective expert policy $\pi^\ast$ through offline RL. This in turn supports accurate loss computation of $q_{\pi^*}(s, a)\left(\pi(a \mid s)-\pi^*(a \mid s)\right)^2$ in Eq. 7.

2. **State Coverage:** 
    - **Question and Analysis:** An intriguing observation is that the low-quality $\\mathcal{D}\_\texttt{off}$ with better state coverage (such as M-R data) can result in superior OBD performance. The question arises: **how does state coverage benefit OBD**? Our analysis suggests that due to optimization errors in OBD, policies trained on distilled data may not perfectly fit the original dataset $\\mathcal{D}\_\texttt{off}$, but rather with a small error. Thus, **OBD performance, or policy training w.r.t. distilled data, can be likened to behavioral cloning (BC) on a noise-version of $\\mathcal{D}\_\texttt{off}$.** 
    - **Experiments and Results:** We conducted BC on the initial data with varying levels of action noise, as detailed in Table 1 of the PDF. The findings show that when there is little to no action noise (noise ratio $\leq 0.05$), higher-quality datasets (M-E) lead to better policy performance compared to datasets with better state coverage (M-R). However, as the noise ratio increases, datasets with better state coverage (M-R) demonstrate greater resilience and outperform the higher-quality datasets (M-E).
    - **Conclusion:** These experiments demonstrate that state coverage enhances robustness against data noise, which partially explains the advantages of state coverage in OBD.

Meta-review: The paper studies the problem of behavior distillation in an offline setting. The reviewers all agree on the contribution of the paper. I recommend acceptance.
Decision: Accept (poster)