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# Momentum-Based Policy Gradient Methods

ICML, pp.4422-4433, (2020)

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摘要

In the paper, we propose a class of efficient momentum-based policy gradient methods for the model-free reinforcement learning, which use adaptive learning rates and do not require any large batches. Specifically, we propose a fast important-sampling momentum-based policy gradient (IS-MBPG) method based on a new momentum-based variance ...更多

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简介

- Reinforcement Learning (RL) has achieved great success in solving many sequential decision-making problems such as autonomous driving (Shalev-Shwartz et al, 2016), robot manipulation (Deisenroth et al, 2013), the game of Go (Silver et al, 2017) and natural language processing (Wang et al, 2018).
- RL involves a Markov decision process (MDP), where an agent takes actions dictated by a policy in a stochastic environment over a sequence of time steps, and maximizes the long-term cumulative rewards to obtain an optimal policy.
- To obtain the optimal policy, policy gradient methods directly maximize the expected total reward ( called as performance function J(θ)) via using the stochastic first-order gradient of cumulative rewards.
- The policy π(a|s) at the state s is represented by a conditional probability distribution πθ(a|s) associated to the parameter θ ∈ Rd

重点内容

- Reinforcement Learning (RL) has achieved great success in solving many sequential decision-making problems such as autonomous driving (Shalev-Shwartz et al, 2016), robot manipulation (Deisenroth et al, 2013), the game of Go (Silver et al, 2017) and natural language processing (Wang et al, 2018)
- Since the classic policy gradient methods (e.g., REINFORCE (Williams, 1992), PGT (Sutton et al, 2000), GPOMDP (Baxter & Bartlett, 2001) and TRPO (Schulman et al, 2015a)) approximate the gradient of the expected total reward based on a batch of sampled trajectories, they generally suffer from large variance in the estimated gradients, which results in a poor convergence
- Our main contributions are summarized as follows: 1) We propose a fast important-sampling momentumbased policy gradient (IS-MBPG) method with adaptive learning rate, which builds on a new momentumbased variance reduction technique of STORM/HybridSGD (Cutkosky & Orabona, 2019; Tran-Dinh et al, 2019) and the importance sampling technique
- Hessian-aided momentum-based policy gradient performs similar compared to Stochastic Recursive Variance Reduced Policy Gradient and Hessian Aided Policy Gradient, though it has an advantage at the beginning
- We proved that the important-sampling momentum-based policy gradient* reaches the best known sample complexity of O( −3) only required one trajectory at each iteration

方法

- The authors demonstrate the performance of the algorithms on four standard reinforcement learning tasks, which are CartPole, Walker, HalfCheetah and Hopper.
- The first one is a discrete task from classic control, and the later three tasks are continuous RL task, which are popular MuJoCo environments (Todorov et al, 2012)
- Detailed description of these environments is shown in Fig. 1.
- The authors' code is publicly available on https://github.com/gaosh/MBPG

结果

- The results of experiments are presented in Fig. 2.
- In the CartPole environment, the IS-MBPG and HA-MBPG algorithms have better performances than the other methods.
- The authors' IS-MBPG algorithm achieves the best final performance with a obvious margin.
- HA-MBPG performs similar compared to SRVR-PG and HAPG, though it has an advantage at the beginning.
- In Hopper environment, the ISMBPG and HA-MBPG algorithms are significantly faster compared to all other methods, while the final average reward are similar for different algorithms.
- In HalfCheetah environment, IS-MBPG, HA-MBPG and SRVR-PG performs at the beginning.
- One possible reason for this observation is that the authors use the estimated Hessian vector product instead of the exact Hessian vector product in HA-MBPG algorithm, which brings additional estimation error to the algorithm

结论

- The authors proposed a class of efficient momentumbased policy gradient methods (i.e., IS-MBPG and HAMBPG), which use adaptive learning rates and do not require any large batches.
- The authors proved that both IS-MBPG and HA-MBPG methods reach the best known sample complexity of O( −3), which only require one trajectory at each iteration.
- The authors proved that the IS-MBPG* reaches the best known sample complexity of O( −3) only required one trajectory at each iteration

总结

## Introduction:

Reinforcement Learning (RL) has achieved great success in solving many sequential decision-making problems such as autonomous driving (Shalev-Shwartz et al, 2016), robot manipulation (Deisenroth et al, 2013), the game of Go (Silver et al, 2017) and natural language processing (Wang et al, 2018).- RL involves a Markov decision process (MDP), where an agent takes actions dictated by a policy in a stochastic environment over a sequence of time steps, and maximizes the long-term cumulative rewards to obtain an optimal policy.
- To obtain the optimal policy, policy gradient methods directly maximize the expected total reward ( called as performance function J(θ)) via using the stochastic first-order gradient of cumulative rewards.
- The policy π(a|s) at the state s is represented by a conditional probability distribution πθ(a|s) associated to the parameter θ ∈ Rd
## Methods:

The authors demonstrate the performance of the algorithms on four standard reinforcement learning tasks, which are CartPole, Walker, HalfCheetah and Hopper.- The first one is a discrete task from classic control, and the later three tasks are continuous RL task, which are popular MuJoCo environments (Todorov et al, 2012)
- Detailed description of these environments is shown in Fig. 1.
- The authors' code is publicly available on https://github.com/gaosh/MBPG
## Results:

The results of experiments are presented in Fig. 2.- In the CartPole environment, the IS-MBPG and HA-MBPG algorithms have better performances than the other methods.
- The authors' IS-MBPG algorithm achieves the best final performance with a obvious margin.
- HA-MBPG performs similar compared to SRVR-PG and HAPG, though it has an advantage at the beginning.
- In Hopper environment, the ISMBPG and HA-MBPG algorithms are significantly faster compared to all other methods, while the final average reward are similar for different algorithms.
- In HalfCheetah environment, IS-MBPG, HA-MBPG and SRVR-PG performs at the beginning.
- One possible reason for this observation is that the authors use the estimated Hessian vector product instead of the exact Hessian vector product in HA-MBPG algorithm, which brings additional estimation error to the algorithm
## Conclusion:

The authors proposed a class of efficient momentumbased policy gradient methods (i.e., IS-MBPG and HAMBPG), which use adaptive learning rates and do not require any large batches.- The authors proved that both IS-MBPG and HA-MBPG methods reach the best known sample complexity of O( −3), which only require one trajectory at each iteration.
- The authors proved that the IS-MBPG* reaches the best known sample complexity of O( −3) only required one trajectory at each iteration

- Table1: Convergence properties of the representative variance-reduced policy algorithms on the non-oblivious model-free RL problem for finding an -stationary point of the nonconcave performance function J(θ), i.e., E ∇J(θ) ≤ . Our algorithms (IS-MBPG, IS-MBPG* and HA-MBPG) and REINFORCE are single-loop algorithms, while the other algorithms are double-loops, which need the outer-loop and inner-loop mini-batch sizes. Note that <a class="ref-link" id="cPapini_et+al_2018_a" href="#rPapini_et+al_2018_a">Papini et al (2018</a>) only remarked that apply the ADAM algorithm (<a class="ref-link" id="cKingma_2014_a" href="#rKingma_2014_a">Kingma & Ba, 2014</a>) to the SVRPG algorithm to obtain an adaptive learning rate, but did not provide any theoretical analysis about this learning rate

基金

- This work was partially supported by U.S NSF IIS 1836945, IIS 1836938, IIS 1845666, IIS 1852606, IIS 1838627, IIS 1837956

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