IMPACT: IMPORTANCE WEIGHTED ASYNCHRONOUS ARCHITECTURES WITH CLIPPED TARGET NETWORKS
Year: 2020

Abstract:
The practical usage of reinforcement learning agents is often bottlenecked by the duration of training time. To accelerate training, practitioners often turn to distributed reinforcement learning architectures to parallelize and accelerate the training process. However, modern methods for scalable reinforcement learning (RL) often tradeoff between the throughput of samples that an RL agent can learn from (sample throughput) and the quality of learning from each sample (sample efficiency). In these scalable RL architectures, as one increases sample throughput (i.e. increasing parallelization in IMPALA (Espeholt et al., 2018)), sample efficiency drops significantly. To address this, we propose a new distributed reinforcement learning algorithm, IMPACT. IMPACT extends IMPALA with three changes: a target network for stabilizing the surrogate objective, a circular buffer, and truncated importance sampling. In discrete action-space environments, we show that IMPACT attains higher reward and, simultaneously, achieves up to 30% decrease in training wall-time than that of IMPALA. For continuous control environments, IMPACT trains faster than existing scalable agents while preserving the sample efficiency of synchronous PPO.

heading: 1 INTRODUCTION
text: Proximal Policy Optimization (Schulman et al., 2017) is one of the most sample-efficient on-policy algorithms. However, it relies on a synchronous architecture for collecting experiences, which is closely tied to its trust region optimization objective. Other architectures such as IMPALA can achieve much higher throughputs due to the asynchronous collection of samples from workers. Yet, IMPALA suffers from reduced sample efficiency since it cannot safely take multiple SGD steps per batch as PPO can. The new agent, Importance Weighted Asynchronous Architectures with Clipped Target Networks (IMPACT), mitigates this inherent mismatch. Not only is the algorithm highly sample efficient, it can learn quickly, training 30 percent faster than IMPALA. At the same time, we propose a novel method to stabilize agents in distributed asynchronous setups and, through our ablation studies, show how the agent can learn in both a time and sample efficient manner.
In our paper, we show that the algorithm IMPACT realizes greater gains by striking the balance between high sample throughput and sample efficiency. In our experiments, we demonstrate in the experiments that IMPACT exceeds state-of-the-art agents in training time (with same hardware) while maintaining similar sample efficiency with PPO’s. The contributions of this paper are as follows:
1. We show that when collecting experiences asynchronously, introducing a target network allows for a stabilized surrogate objective and multiple SGD steps per batch (Section 3.1).
2. We show that using a circular buffer for storing asynchronously collected experiences allows for smooth trade-off between real-time performance and sample efficiency (Section 3.2).
3. We show that IMPACT, when evaluated using identical hardware and neural network models, improves both in real-time and timestep efficiency over both synchronous PPO and IMPALA (Section 4).

heading: 2 BACKGROUND
text: Reinforcement Learning assumes a Markov Decision Process (MDP) setup defined by the tuple (S,A, p, γ, r) where S and A represent the state and action space, γ ∈ [0, 1] is the discount factor, and p : S ×A× S → R and R : S ×A→ R are the transition dynamics and reward function that models an environment.
Let π(at|st) : S ×A→ [0, 1] denote a stochastic policy mapping that returns an action distribution given state st ∈ S. Rolling out policy π(at|st) in the environment is equivalent to sampling a trajectory τ ∼ P(τ ), where τ := (s0, a0, ...., aT−1, sT , aT ). We can compactly define state and state-action marginals of the trajectory distribution pπ(st) and pπ(st, at) induced by the policy π(at|st).The goal for reinforcement learning aims to maximize the following objective: J(θ) = E(st,at)∼pπ [ ∑T t=0 γ tR(st, at)].
When θ parameterizes π(at|st), the policy is updated according to the Policy Gradient Theorem (Sutton et al., 2000):
∇θJ(θ) = E(st,at)∼pπ(·) [ ∇θ log πθ(at|st)Âπθ (st, at) ] ,
where Âπθ (st, at) is an estimator of the advantage function. The advantage estimator is usually defined as the 1-step TD error, Âπθ (st, at) = r(st, at) + γV̂ (st+1) − V̂ (st), where V̂ (st) is an estimation of the value function. Policy gradients, however, suffer from high variance and large update-step sizes, oftentimes leading to sudden drops in performance.

heading: 2.1 DISTRIBUTED PPO
text: Per iteration, Proximal Policy Optimization (PPO) optimizes policy πθ from target πθold via the following objective function
L(θ) = Epπθold
[ min ( rt(θ)Ât, clip (rt(θ), 1− , 1 + ) Ât )] ,
where rt(θ) = πθ(at|st) πθold (at|st) and is the clipping hyperparameter. In addition, many PPO implementations use GAE-λ as a low bias, low variance advantage estimator for Ât (Schulman et al., 2015b). PPO’s surrogate objective contains the importance sampling ratio rt(θ), which can potentially explode if πθold is too far from πθ. (Han & Sung, 2017). PPO’s surrogate loss mitigates this with the clipping function, which ensures that the agent makes reasonable steps. Alternatively, PPO can also be seen as an adaptive trust region introduced in TRPO (Schulman et al., 2015a).
In Figure 1a, distributed PPO agents implement a synchronous data-gathering scheme. Before data collection, workers are updated to πold and aggregate worker batches to training batch Dtrain. The learner performs many mini-batch gradient steps on Dtrain. Once the learner is done, learner weights are broadcast to all workers, who start sampling again.

heading: 2.2 IMPORTANCE WEIGHTED ACTOR-LEARNER ARCHITECTURES
text: In Figure 1b, IMPALA decouples acting and learning by having the learner threads send actions, observations, and values while the master thread computes and applies the gradients from a queue of learners experience (Espeholt et al., 2018). This maximizes GPU utilization and allows for increased sample throughput, leading to high training speeds on easier environments such as Pong. As the number of learners grows, worker policies begin to diverge from the learner policy, resulting in stale policy gradients. To correct this, the IMPALA paper utilizes V-trace to correct the distributional shift:
vst = Vφ (st) + t+n−1∑ i=t γi−t i−1∏ j=t cj  ρi (ri+1 + γVφ (si+1)− Vφ (si)) where, Vφ is the value network, πθ is the policy network of the master thread, µθ′ is the policy
network of the learner thread, and cj = min ( c̄,
πθ(aj |sj) µθ′ (aj |sj)
) and ρi = min ( ρ̄, πθ(ai|si)µθ′ (ai|si) ) are clipped
IS ratios.
Algorithm 1 IMPACT Input: Batch size M , number of workers W , circular buffer size N , replay coefficient K, target
update frequency ttarget, weight broadcast frequency tfrequency, learning rates α and β 1: Randomly initialize network weights (θ, w) 2: Initialize target network (θ′, w′)← (θ, w) 3: Create W workers and duplicate (θ, w) to each worker 4: Initialize circular buffer C(N,K) 5: for t = 1, .., T do 6: Obtain batch B of size M traversed k times from C(N,K) 7: If k = 0, evaluate B on target θ′, append target output to B 8: Compute policy and value network gradients
∇θJ(θ) = 1
M ∑ (i,j)∈B ∇θπθ(sj |aj) max(πtarget(sj |aj), βπworkeri(sj |aj)) ÂV -GAE − η∇θKL (πtarget , πθ)
∇wL(w) = 1
M ∑ j (Vw(sj)− V̂V -GAE(sj))∇wVw(sj)
9: Update policy and value network weights θ ← θ + αt∇θJ(θ),w ← w − βt∇wL(w) 10: If k = K, discard batch B from C(N,K) 11: If t ≡ 0 (mod ttarget), update target network (θ′, w′)← (θ, w) 12: If t ≡ 0 (mod tfrequency), broadcast weights to workers 13: end for
Worker-i Input: Worker sample batch size S
1: repeat 2: Bi = ∅ 3: for t = 1, ..., S do 4: Store (st, at, rt, st+1) ran by θi in batch Bi 5: end for 6: Send Bi to C(N,K) 7: If broadcasted weights exist, set θi ← θ 8: until learner finishes

heading: 3 IMPACT ALGORITHM
text: Like IMPALA, IMPACT separates sampling workers from learner workers. Algorithm 1 and Figure 1c describe the main training loop and architecture of IMPACT. In the beginning, each worker copies weights from the master network. Then, each worker uses their own policy to collect trajectories
and sends the data (st, at, rt) to the circular buffer. Simultaneously, workers also asynchronously pull policy weights from the master learner. In the meantime, the target network occasionally syncs with the master learner every ttarget iterations. The master learner then repeatedly draws experience from the circular buffer. Each sample is weighted by the importance ratio of πθπworkeri as well as clipped with target network ratio πworkeriπtarget . The target network is used to provide a stable trust region (Figure 2), allowing multiple steps per batch (i.e., like PPO) even in the asynchronous setting (i.e., with the IMPALA architecture). In the next section, we describe the design of this improved objective.

heading: 3.1 MAXIMAL TARGET-WORKER CLIPPING
text: PPO gathers experience from previous iteration’s policy πθold , and the current policy trains by importance sampling off-policy experience with respect to πθ. In the asynchronous setting, worker i’s policy, denoted as πworkeri , generates experience for the policy network πθ. The probability that batch B comes from worker i can be parameterized as a categorical distribution i ∼ D(α1, ..., αn). We include this by adding an extra expectation to the importance-sampled policy gradient objective (IS-PG) (Jie & Abbeel, 2010):
JIS(θ) = Ei∼D(α) [ E(st,at)∼πworkeri [ πθ
πworkeri Ât
]] .
Since each worker contains a different policy, the agent introduces a target network for stability (Figure 2). Off-policy agents such as DDPG and DQN update target networks with a moving average. For IMPACT, we periodically update the target network with the master network. However, training with importance weighted ratio πθπtarget can lead to numerical instability, as shown in Figure 3. To prevent this, we clip the importance sampling ratio from worker policy,πworkeri , to target policy, πtarget:
JAIS(θ) = Ei∼D(α) [ E(st,at)∼πworkeri [ min( πworkeri πtarget , ρ) πθ πworkeri Ât ]] = Ei∼D(α) [ E(st,at)∼πworkeri [ πθ
max(πtarget, βπworkeri) Ât
]] ,
where β = 1ρ . In the experiments, we set ρ as a hyperparameter with ρ ≥ 1 and β ≤ 1. To see why clipping is necessary, when master network’s action distribution changes significantly over few training iterations, worker i’s policy, πworkeri , samples data outside that of target policy, πtarget, leading to large likelihood ratios,
πworkeri πtarget . The clipping function min(πworkeriπtarget , ρ) pulls back
πworkeri
, R3 = πθmax(πtarget,βπworkeri )
. In (b),
we show the target network update frequency is robust to a range of choices. We try target network update frequency ttarget equal to the multiple (ranging from 1/16 and 16) of n = N ·K, the product of the size of circular buffer and the replay times for each batch in the buffer.
large IS ratios to ρ. Figure 10 in Appendix E provides additional intuition behind the target clipping objective. We show that the target network clipping is a lower bound of the IS-PG objective.
For ρ > 1, the clipped target ratio is larger and serves to augment advantage estimator Ât. This incentivizes the agent toward good actions while avoiding bad actions. Thus, higher values of ρ encourages the agent to learn faster at the cost of instability.
We use GAE-λ with V-trace (Han & Sung, 2019). The V-trace GAE-λ modifies the advantage function by adding clipped importance sampling terms to the summation of TD errors:
ÂV -GAE = t+n−1∑ i=t (λγ)i−t i−1∏ j=t cj  δiV, where ci = min ( c̄,
πtarget(aj |sj) πworkeri (aj |sj)
) (we use the convention ∏t−1 j=t cj = 1) and δiV is the importance
sampled 1-step TD error introduced in V-trace.

heading: 3.2 CIRCULAR BUFFER
text: IMPACT uses a circular buffer (Figure 4) to emulate the mini-batch SGD used by standard PPO. The circular buffer stores N batches that can be traversed at max K times. Upon being traversed K times, a batch is discarded and replaced by a new worker batch.
For motivation, the circular buffer and the target network are analogous to mini-batching from πold experience in PPO. When target network’s update frequency n = NK, the circular buffer is equivalent to distributed PPO’s training batch when the learner samples N minibatches for K SGD iterations.
This is in contrast to standard replay buffers, such as in ACER and APE-X, where transitions (st, at, rt, st+1) are either uniformly sampled or sampled based on priority, and, when the buffer is full, the oldest transitions are discarded (Wang et al., 2016; Horgan et al., 2018).
Figure 4 illustrates an empirical example where tuning K can increase training sample efficiency and decrease training wall-clock time.

heading: 4 EVALUATION
text: In our evaluation we seek to answer the following questions:
1. How does the target-clipping objective affect the performance of the agents compared to prior work? (Section 4.1)
2. How does the IMPACT circular buffer affect sample efficiency and training wall-clock time? (Section 4.2)
3. How does IMPACT compare to PPO and IMPALA baselines in terms of sample and real-time performance? (Section 4.3)
4. How does IMPACT scale with respect to the number of workers? (Section 4.4)

heading: 4.1 TARGET CLIPPING PERFORMANCE
text: We investigate the performance of the clipped-target objective relative to prior work, which includes PPO and IS-PG based objectives. Specifically, we consider the following ratios below:
R1 = πθ πtarget R2 = πθ πworkeri R3 = πθ max(πtarget,βπworkeri )
For all three experiments, we truncate all three ratios with PPO’s clipping function: c(R) = clip(R, 1− , 1+ ) and train in an asynchronous setting. Figure 4(a) reveals two important takeaways: first, R1 suffers from sudden drops in performance midway through training. Next, R2 trains stably but does not achieve good performance.
We theorize that R1 fails due to the target and worker network mismatch. During periods of training where the master learner undergoes drastic changes, worker action outputs vastly differ from the learner outputs, resulting in small action probabilities. This creates large ratios in training and destabilizes training. We hypothesize that R2 fails due to different workers pushing and pulling the learner in multiple directions. The learner moves forward with the most recent worker’s suggestions without developing a proper trust region, resulting in many worker’s suggestions conflicting with each other.
The loss function, R3 shows that clipping is necessary and can help facilitate training. By clipping the target-worker ratio, we make sure that the ratio does not explode and destabilize training. Furthermore, we prevent workers from making mutually destructive suggestions by having a target network provide singular guidance.

heading: 4.1.1 TARGET NETWORK UPDATE FREQUENCY
text: In Section 3.2, an analogy was drawn between PPO’s mini-batching mechanism and the circular buffer. Our primary benchmark for target update frequency is n = N ·K, where N is circular buffer size and K is maximum replay coefficient. This is the case when PPO is equivalent to IMPACT.
In Figure 4(b), we test the frequency of updates with varying orders of magnitudes of n. In general, we find that agent performance is robust to vastly differing frequencies. However, when n = 1 ∼ 4,
the agent does not learn. Based on empirical results, we theorize that the agent is able to train as long as a stable trust region can be formed. On the other hand, if update frequency is too low, the agent is stranded for many iterations in the same trust region, which impairs learning speed.

heading: 4.2 TIME AND SAMPLE EFFICIENCY WITH CIRCULAR BUFFER
text: Counter to intuition, the tradeoff between time and sample efficiency when K increases is not necessarily true. In Figure 4b and 4c, we show that IMPACT realizes greater gains by striking the balance between high sample throughput and sample efficiency. When K = 2, IMPACT performs the best in both time and sample efficiency. Our results reveal that wall-clock time and sample efficiency can be optimized based on tuning values of K in the circular buffer.

heading: 4.3 COMPARISON WITH BASELINES
text: We investigate how IMPACT attains greater performance in wall clock-time and sample efficiency compared with PPO and IMPALA across six different continuous control and discrete action tasks.
We tested the agent on three continuous environments (Figure 5): HalfCheetah, Hopper, and Humanoid on 16 CPUs and 1 GPU. The policy networks consist of two fully-connected layers of 256 units with nonlinear activation tanh. The critic network shares the same architecture as the policy network. For consistentency, same network architectures were employed across PPO, IMPALA, and IMPACT.
For the discrete environments (Figure 6), Pong, SpaceInvaders, and Breakout were chosen as common benchmarks used in popular distributed RL libraries (Caspi et al., 2017; Liang et al., 2018). Additional experiments for discrete environments are in the Appendix. These experiments were ran on 32 CPUs and 1 GPU. The policy network consists of three 4x4 and one 11x11 conv layer, with nonlinear activation ReLU. The critic network shares weights with the policy network. The input of the network is a stack of four 42x42 down-sampled images of the Atari environment. The hyper-parameters for continuous and discrete environments are listed in the Appendix B table 1 and 2 respectively.
Figures 5 and 6 show the total average return on evaluation rollouts for IMPACT, IMPALA and PPO. We train each algorithm with three different random seeds on each environment for a total time
of three hours. According to the experiments, IMPACT is able to train much faster than PPO and IMPALA in both discrete and continuous domains, while preserving same or better sample efficiency than PPO.
Our results reveal that continuous control tasks for IMPACT are sensitive to the tuple (N,K) for the circular buffer. N = 16 and K = 20 is a robust choice for continuous control. Although higher K inhibits workers’ sample throughput, increased sample efficiency from replaying experiences results in an overall reduction in training wall-clock time and higher reward. For discrete tasks, N = 1 and K = 2 works best. Empirically, agents learn faster from new experience than replaying old experience, showing how exploration is crucial to achieving high asymptotic performance in discrete enviornments.

heading: 4.4 IMPACT SCALABILITY
text: Figure 7 shows how IMPACT’s performance scales relative to the number of workers. More workers means increased sample throughput, which in turn increases training throughput (the rate that learner consumes batches). With the learner consuming more worker data per second, IMPACT can attain better performance in less time. However, as number of workers increases, observed increases in performance begin to decline.

heading: 5 RELATED WORK
text: Distributed RL architectures are often used to accelerate training. Gorila (Nair et al., 2015) and A3C (Mnih et al., 2016) use workers to compute gradients to be sent to the learner. A2C (Mnih et al., 2016) and IMPALA (Espeholt et al., 2018) send experience tuples to the learner. Distributed replay buffers, introduced in ACER (Wang et al., 2016) and Ape-X (Horgan et al., 2018), collect worker-collected experience and define an overarching heuristic for learner batch selection. IMPACT is the first to fully incorporate the sample-efficiency benefits of PPO in an asynchronous setting.
Surreal PPO (Fan et al., 2018) also studies training with PPO in the asynchronous setting, but do not consider adaptation of the surrogate objective nor IS-correction. Their use of a target network for broadcasting weights to workers is also entirely different from IMPACT’s. Consequently, IMPACT is able to achieve better results in both real-time and sample efficiency.
Off-policy methods, including DDPG and QProp, utilize target networks to stabilize learning the Q function (Lillicrap et al., 2015; Gu et al., 2016). This use of a target network is related but different from IMPACT, which uses the network to define a stable trust region for the PPO surrogate objective.

heading: 6 CONCLUSION
text: In conclusion, we introduce IMPACT, which extends PPO with a stabilized surrogate objective for asynchronous optimization, enabling greater real-time performance without sacrificing timestep efficiency. We show the importance of the IMPACT objective to stable training, and show it can outperform tuned PPO and IMPALA baselines in both real-time and timestep metrics.

heading: A ADDITIONAL EXPERIMENTS

heading: B HYPER PARAMETERS FOR ALL ENVIRONMENTS
text: B.1 DISCRETE ENVIRONMENTS
B.2 CONTINUOUS ENVIRONMENTS
B.3 HYPERPARAMETER BUDGET
Listed below was the grid search we used for each algorithm to obtain optimal hyperparameters. Optimal values were found via grid searching on each hyperparameter separately. We found that IMPACT’s optimal hyperparameter values tend to hover close to either IMPALA’s or PPO’s, which greatly mitigated IMPACT’s budget.
B.3.1 DISCRETE ENVIRONMENT SEARCH
1For HalfCheetah-v2, IMPACT and PPO Num SGD Iterations (K) is 32. 2For HalfCheetah-v2, IMPACT Value Function Coeff is 0.5. 3IMPALA was difficult to finetune due to unstable runs.
B.4 CONTINUOUS ENVIRONMENT SEARCH
C IMPALA TO IMPACT
In Figure 9, we gradually add components to IMPALA until the agent is equivalent to IMPACT’s. Starting from IMPALA, we gradually add PPO’s objective function, circular replay buffer, and target-worker clipping. In particular, IMPALA with PPO’s objective function and circular replay buffer is equivalent to an asynchronous-variant of PPO (APPO). APPO fails to perform as well as synchronous distributed PPO, since PPO is an on-policy algorithm.
D IMPALA IN CONTINUOUS ENVIRONMENTS
In Figure 6, IMPALA performs substantially worse than other agents in continuous environments. We postulate that IMPALA suffers from low asymptotic performance here since its objective is an importance-sampled version of the Vanilla Policy Gradient (VPG) objective, which is known to suffer from high variance and large update-step sizes. We found that for VPG, higher learning rates encourage faster learning in the beginning but performance drops to negative return later in training.
In Appendix B, for IMPALA, we heavily tuned on the learning rate, finding that small learning rates stabilize learning at the cost of low asymptotic performance. Prior work also reveals the agents that use VPG fail to attain good performance in non-trivial continuous tasks (Achiam, 2018). Our results with IMPALA reaches similar performance compared to other VPG-based algorithms. The closest neighbor to IMPALA, A3C uses workers to compute gradients from the VPG objective to send to the learner thread. A3C performs well in InvertedPendulum yet flounders in continuous environments (Tassa et al., 2018).

heading: E THE INTUITION OF THE OBJECTIVE
text: The following ratios represent the objective functions for different ablation studies. In the plots (Figure 10), we set the advantage function to be one, i.e. Ât = 1.
• IS ratio: πθπworkeri Ât • IMPACT target: min ( πworkeri πtarget , ρ ) πθ πworkeri Ât
• PPO -clip: min (
πθ πworkeri Ât, clip( πθπworkeri , 1− , 1 + )Ât ) • IMPACT target -clip: min ( min ( πworkeri πtarget , ρ ) πθ πworkeri Ât, clip ( min ( πworkeri πtarget , ρ ) πθ πworkeri , 1− , 1 + ) Ât
) According to Figure 10, IS ratio is large when πworkeri assigns low probability. IMPACT target -clip is a lower bound of the PPO -clip. In an distributed asynchronous setting, the trust region suffers from larger variance stemming from off-policy data. IMPACT target -clip ratio mitigates this by encouraging conservative and reasonable policy-gradient steps.

Review summaries:
This paper introduces IMPACT which is a distributed RL algorithm that shortens training time of RL systems while maintaining/ improving the sample efficiency. It is built on top of the famous PPO algorithm (https://arxiv.org/abs/1707.06347). The authors break down the novel component of their model into three categories: target network, circular buffer, and importance sampling. They evaluate the effectiveness of each component through different experiments. 

Reinforcement learning (RL) training speed is broadly evaluated on two dimensions:  sample efficiency (the number of environment interactions required) and wall-clock time.  Improved wall-clock training time has been achieved through distributed actors and learners, but often at the expense of sample efficiency.  IMPACT repurposes successful concepts from deep RL - the target network, importance sampling and a replay buffer to demonstrate improvements on both axes in on three continuous environments and three games from the Atari Learning Environment.