Model-free reinforcement learning methods have successfully been applied to practical applications such as decision-making problems in Atari games. However, these methods have inherent shortcomings, such as a high variance and low sample efficiency. To improve the policy performance and sample efficiency of model-free reinforcement learning, we propose proximal policy optimization with model-based methods (PPOMM), a fusion method of both model-based and model-free reinforcement learning. PPOMM not only considers the information of past experience but also the prediction information of the future state. PPOMM adds the information of the next state to the objective function of the proximal policy optimization (PPO) algorithm through a model-based method. This method uses two components to optimize the policy: the error of PPO and the error of model-based reinforcement learning. We use the latter to optimize a latent transition model and predict the information of the next state. For most games, this method outperforms the state-of-the-art PPO algorithm when we evaluate across 49 Atari games in the Arcade Learning Environment (ALE). The experimental results show that PPOMM performs better or the same as the original algorithm in 33 games.
SuttonR.S. and BartoA.G., Reinforcement learning: An introduction[M], MIT press, (2018).
2.
HendersonP., IslamR., BachmanP., et al., Deep reinforcement learning that matters[C], Proceedings of the AAAI conference on artificial intelligence32(1) (2018).
3.
HintonG.E. and SalakhutdinovR.R., Reducing the dimensionality of data with neural networks[J], Science313(5786) (2006), 504–507.
4.
HintonG.E., OsinderoS. and TehY.W., A fast learning algorithm for deep belief nets[J], Neural Computation18(7) (2006), 1527–1554.
5.
KrizhevskyA., SutskeverI. and HintonG.E., ImageNet classification with deep convolutional neural networks[J], Communications of the ACM60(6) (2017), 84–90.
6.
SimonyanK. and ZissermanA., Very deep convolutional networks for large-scale image recognition[J], arXiv preprint arXiv:1409.1556, (2014).
7.
HeK., ZhangX., RenS., et al., Deep residual learning for image recognition[C], Proceedings of the IEEE conference on computer vision and pattern recognition2016770–778.
8.
GravesA., MohamedA. and HintonG., Speech recognition with deep recurrent neural networks[C], 2013 IEEE international conference on acoustics, speech and signal processing. Ieee20136645–6649.
9.
GravesA. and JaitlyN., Towards end-to-end speech recognition with recurrent neural networks[C], International conference on machine learning. PMLR20141764–1772.
10.
CaiQ., YangZ., SzepesvariC., et al., Optimistic Policy Optimization with General Function Approximations[J], (2020).
11.
YoungK., WangB. and TaylorM.E., Metatrace: Online step-size tuning by meta-gradient descent for reinforcement learning control[J], arXiv preprint arXiv:1805.04514, (2018).
12.
MnihV., KavukcuogluK., SilverD., et al., Human-level control through deep reinforcement learning[J], Nature518(7540): (2015), 529–533.
13.
WangZ., SchaulT., HesselM., et al., Dueling network architectures for deep reinforcement learning[C], International conference on machine learning. PMLR20161995–2003.
14.
MnihV., BadiaA.P., MirzaM., et al., Asynchronous methods for deep reinforcement learning[C], International conference on machine learning. PMLR20161928–1937.
15.
GuS., LillicrapT., SutskeverI., et al., Continuous deep q-learning with model-based acceleration[C], International conference on machine learning. PMLR20162829–2838.
16.
SchulmanJ., LevineS., AbbeelP., et al., Trust region policy optimization[C], International conference on machine learning. PMLR20151889–1897.
17.
SilverD., HuangA., MaddisonC.J., et al., Mastering the game of Go with deep neural networks and tree search[J], Nature529(7587) (2016), 484–489.
18.
HaarnojaT., ZhouA., AbbeelP., et al., Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor[C], International conference on machine learning. PMLR20181861–1870.
19.
ZhangZ., ZhouY. and JiX., Model-free reinforcement learning: from clipped pseudo-regret to sample complexity[C], International Conference on Machine Learning. PMLR202112653–12662.
20.
MesnardT., WeberT., ViolaF., et al., Counterfactual credit assignment in model-free reinforcement learning[J], arXiv preprint arXiv:2011.09464, (2020).
21.
FarinaG. and SandholmT., Model-Free Online Learning in Unknown Sequential Decision Making Problems and Games[J], arXiv preprint arXiv:2103.04539, (2021).
22.
MesnardT., WeberT., ViolaF., et al., Model-Free Counterfactual Credit Assignment[J], (2020).
23.
KhoiN.D.H., VanC P., TranH.V., et al., Multi-Objective Exploration for Proximal Policy Optimization[C], 2020 Applying New Technology in Green Buildings (ATiGB). IEEE2021105–109.
24.
van Martijn OtterloW.M., Reinforcement Learning[J], (2012).
25.
FanY. and MingY., Model-based Reinforcement Learning for Continuous Control with Posterior Sampling[C], International Conference on Machine Learning. PMLR20213078–3087.
26.
YildizC., HeinonenM. and LähdesmäkiH., Continuous-time Model-based Reinforcement Learning[C], International Conference on Machine Learning. PMLR202112009–12018.
27.
RybkinO., ZhuC., NagabandiA., et al., Model-based reinforcement learning via latent-space collocation[C], International Conference on Machine Learning. PMLR20219190–9201.
28.
SongY. and SunW., Pc-mlp: Model-based reinforcement learning with policy cover guided exploration[C], International Conference on Machine Learning. PMLR20219801–9811.
29.
HongJ., WangH., WangZ., et al., Learning Model-Based Privacy Protection under Budget Constraints[C], The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21)35(9) (2021).
30.
MatsushimaT., FurutaH., MatsuoY., et al., Deployment efficient reinforcement learning via model-based offline optimization[J], arXiv preprint arXiv:2006.03647, (2020).
31.
LiuQ., YuT., BaiY., et al., A sharp analysis of model-based reinforcement learning with self-play[C], International Conference on Machine Learning. PMLR20217001–7010.
32.
LeeB.J., LeeJ. and KimK.E., Representation balancing offline model-based reinforcement learning[C], International Conference on Learning Representations (2020).
33.
NgJ.H.A. and PetrickR.P.A., Incremental Learning of Planning Actions in Model-Based Reinforcement Learning[C], IJCAI.20193195–3201.
34.
RybkinO., ZhuC., NagabandiA., et al., Model-based reinforcement learning via latent-space collocation[C], International Conference on Machine Learning. PMLR20219190–9201.
35.
JordanM.I. and RumelhartD.E., Forward models: Supervised learning with a distal teacher[J], Cognitive Science16(3) (1992), 307–354.
36.
FisacJ.F., AkametaluA.K., ZeilingerM.N., et al., A general safety framework for learning-based control in uncertain robotic systems[J], IEEE Transactions on Automatic Control64(7) (2018), 2737–2752.
37.
SadighD., SastryS., SeshiaS.A., et al., Planning for autonomous cars that leverage effects on human actions[C], Robotics: Science and Systems2 (2016), 1–9.
38.
SunY., YuanX., LiuW., et al., Model-Based Reinforcement Learning via Proximal Policy Optimization[C], 2019 Chinese Automation Congress (CAC). IEEE20194736–4740.
39.
PanF., CaiQ., ZengA.X., et al., Policy optimization with model-based explorations[C], Proceedings of the AAAI Conference on Artificial Intelligence33(01) (2019), 4675–4682.
40.
SeglerM.H.S., PreussM. and WallerM P., Planning chemical syntheses with deep neural networks and symbolic AI[J], Nature555(7698) (2018), 604–610.
41.
SalasD.F. and PowellW.B., Benchmarking a scalable approximate dynamic programming algorithm for stochastic control of multidimensional energy storage problems[J], Dept Oper Res Financial Eng, (2013).
42.
ZhangX., LiuJ., FengJ., et al., Effective capture of nongraspable objects for space robots using geometric cage pairs[J], IEEE/ASME Transactions on Mechatronics25(1) (2019), 95–107.
43.
ZhangX. and LiuJ., Effective motion planning strategy for space robot capturing targets under consideration of the berth position[J], Acta Astronautica148 (2018), 403–416.
44.
YildirimI., WuJ., KanwisherN., et al., An integrative computational architecture for object-driven cortex[J], Current Opinion in Neurobiology55 (2019), 73–81.
45.
HaD. and SchmidhuberJ., Recurrent world models facilitate policy evolution[J], arXiv preprint arXiv:1809.01999, (2018).
46.
VeerapaneniR., Co-ReyesJ.D., ChangM., et al., Entity abstraction in visual model-based reinforcement learning[C], Conference on Robot Learning. PMLR20201439–1456.
47.
WatterM., SpringenbergJ.T., BoedeckerJ., et al., Embed to control: A locally linear latent dynamics model for control control from raw images[J], arXiv preprint arXiv:1506.07365, (2015).
48.
KarlM., SoelchM., BayerJ., et al., Deep variational bayes filters: Unsupervised learning of state space models from raw data[J], arXiv preprint arXiv:1605.06432, 2016.
49.
TodorovE. and LiW., A generalized iterative LQG method for locally-optimal feedback control of constrained nonlinear stochastic systems[C], Proceedings of the American Control Conference, IEEE, 2005 (2005), 300–306.
50.
Van HoofH., ChenN., KarlM., et al., Stable reinforcement learning with autoencoders for tactile and visual data[C], 2016 IEEE/RSJ international conference on intelligent robots and systems (IROS). IEEE, 2016:3928–3934.
51.
ZhangM., VikramS., SmithL., et al., Solar: Deep structured representations for model-based reinforcement learning[C], International Conference on Machine Learning. PMLR, 2019:7444–7453.
52.
FraccaroM, KamronnS, PaquetU, et al., A disentangled recognition and nonlinear dynamics model for unsupervised learning[J], arXiv preprint arXiv:1710.05741, (2017).
53.
O’DohertyJ P, DayanP, FristonK, et al., Temporal difference models and reward-related learning in the human brain[J], Neuron38(2) (2003), 329–337.
54.
SeymourB., O’DohertyJ.P., DayanP., et al., Temporal difference models describe higher-order learning in humans[J], Nature429(6992) (2004), 664–667.
55.
WatkinsC.J.C.H. and DayanP., Q-learning[J], Machine Learning8(3-4) (1992), 279–292.
56.
PeerO., TesslerC., MerlisN., et al., Ensemble Bootstrapping for Q-Learning[J], arXiv preprint arXiv:2103.00445, (2021).
57.
ChenX., WangC., ZhouZ., et al., Randomized ensembled double q-learning: Learning fast without a model[J], arXiv preprint arXiv:2101.05982, (2021).
58.
WangY.H., LiT.H.S. and LinC.J., Backward Q-learning: The combination of Sarsa algorithm and Q-learning[J], Engineering Applications of Artificial Intelligence26(9) (2013), 2184–2193.
59.
ZhaoD., WangH., ShaoK., et al., Deep reinforcement learning with experience replay based on SARSA[C], IEEE, 2016 IEEE Symposium Series on Computational Intelligence (SSCI)20161–6.
60.
SchulmanJ., MoritzP., LevineS., et al., High-dimensional continuous control using generalized advantage estimation[J], arXiv preprint arXiv:1506.02438, (2015).
WuY., ZhaiS., SrivastavaN., et al., Uncertainty Weighted Actor-Critic for Offline Reinforcement Learning[J], arXiv preprint arXiv:2105.08140, (2021).
63.
KhodadadianS., ChenZ. and MaguluriS.T., Finite-Sample Analysis of Off-Policy Natural Actor-Critic Algorithm[J], arXiv preprint arXiv:2102.09318, (2021).
64.
BjörckJ., ChenX., De SaC., et al., Low-Precision Reinforcement Learning: Running Soft Actor-Critic in Half Precision[C], International Conference on Machine Learning. PMLR2021980–991.
65.
WenJ., KumarS., GummadiR., et al., Characterizing the Gap Between Actor-Critic and Policy Gradient[J], arXiv preprint arXiv:2106.06932, (2021).
66.
AndrychowiczM., RaichukA., StańczykP., et al., What matters for on-policy deep actor-critic methods? a large-scale study[C], International Conference on Learning Representations. (2020).
FanZ., SuR., ZhangW., et al., Hybrid actor-critic reinforcement learning in parameterized action space[J], arXiv preprint arXiv:1903.01344, (2019).
69.
LibardiG., De FabritiisG. and DittertS., Guided Exploration with Proximal Policy Optimization using a Single Demonstration[C], International Conference on Machine Learning. PMLR20216611–6620.
70.
HanS. and SungY., Diversity actor-critic: Sample-aware entropy regularization for sample-efficient exploration[C], International Conference on Machine Learning. PMLR20214018–4029.
71.
GuoH., FuZ., YangZ., et al., Decentralized single-timescale actor-critic on zero-sum two-player stochastic games[C], International Conference on Machine Learning. PMLR20213899–3909.
72.
DynaS.R.S., An integrated architecture for learning, planning, and reacting[J], ACM Sigart Bulletin2(4) (1991), 160–163.
73.
PengJ. and WilliamsR.J., Efficient learning and planning within the Dyna framework[J], Adaptive Behavior1(4) (1993), 437–454.
74.
SuttonL.K.R., Model-based reinforcement learning with an approximate, learned model[C], Proceedings of the ninth Yale workshop on adaptive and learning systems1996101–105.
75.
PengB., LiX., GaoJ., et al., Deep dyna-q: Integrating planning for task-completion dialogue policy learning[J], arXiv preprint arXiv:1801.06176, (2018).
76.
FeinbergV., WanA., StoicaI., et al., Model-based value estimation for efficient model-free reinforcement learning[J], arXiv preprint arXiv:1803.00101, (2018).
77.
BuckmanJ., HafnerD., TuckerG., et al., Sample-efficient reinforcement learning with stochastic ensemble value expansion[J], arXiv preprint arXiv:1807.01675, (2018).
78.
OhJ., SinghS. and LeeH., Value prediction network[J], arXiv preprint arXiv:1707.03497, (2017).
79.
MirowskiP., PascanuR., ViolaF., et al., Learning to navigate in complex environments[J], arXiv preprint arXiv:1611.03673, (2016).
80.
BellemareM.G., NaddafY., VenessJ., et al., The arcade learning environment: An evaluation platform for general agents[J], Journal of Artificial Intelligence Research47 (2013), 253–279.
