Abstract
In most high-risk applications, interpretability is crucial for ensuring system safety and trust. However, existing research often relies on hard-to-understand, highly parameterized models, such as neural networks. In this paper, we focus on the problem of policy search in continuous observations and actions spaces. We leverage two graph-based Genetic Programming (GP) techniques—Cartesian Genetic Programming (CGP) and Linear Genetic Programming (LGP)—to develop effective yet interpretable control policies. Our experimental evaluation on eight continuous robotic control benchmarks shows competitive results compared to state-of-the-art Reinforcement Learning (RL) algorithms. Moreover, we find that graph-based GP tends towards small, interpretable graphs even when competitive with RL. By examining these graphs, we are able to explain the discovered policies, paving the way for trustworthy AI in the domain of continuous control.
References
Adadi, A., Berrada, M.: Peeking inside the black-box: a survey on explainable artificial intelligence (XAI). IEEE Access 6, 52138–52160 (2018)
Amaral, R., Ianta, A., Bayer, C., Smith, R.J., Heywood, M.I.: Benchmarking genetic programming in a multi-action reinforcement learning locomotion task. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 522–525 (2022)
Bradbury, J., et al.: Jax: composable transformations of python+ numpy programs (2018)
Brameier, M., Banzhaf, W., Banzhaf, W.: Linear Genetic Programming, vol. 1. Springer, New York (2007). https://doi.org/10.1007/978-0-387-31030-5
Coulom, R.: Reinforcement learning using neural networks, with applications to motor control. Ph.D. thesis, Institut National Polytechnique de Grenoble-INPG (2002)
Custode, L.L., Iacca, G.: Evolutionary learning of interpretable decision trees. arXiv preprint arXiv:2012.07723 (2020)
Custode, L.L., Iacca, G.: Interpretable pipelines with evolutionary optimized modules for reinforcement learning tasks with visual inputs. In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 224–227 (2022)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Ferigo, A., Custode, L.L., Iacca, G.: Quality diversity evolutionary learning of decision trees. arXiv preprint arXiv:2208.12758 (2022)
Ferigo, A., Custode, L.L., Iacca, G.: Quality-diversity optimization of decision trees for interpretable reinforcement learning. Neural Comput. Appl. 1–12 (2023)
Françoso Dal Piccol Sotto, L., Kaufmann, P., Atkinson, T., Kalkreuth, R., Porto Basgalupp, M.: Graph representations in genetic programming. Genet. Program. Evolvable Mach. 22(4), 607–636 (2021)
Freeman, C.D., Frey, E., Raichuk, A., Girgin, S., Mordatch, I., Bachem, O.: Brax-a differentiable physics engine for large scale rigid body simulation. arXiv preprint arXiv:2106.13281 (2021)
Glanois, C., Weng, P., Zimmer, M., Li, D., Yang, T., Hao, J., Liu, W.: A survey on interpretable reinforcement learning. arXiv preprint arXiv:2112.13112 (2021)
Glass, A., McGuinness, D.L., Wolverton, M.: Toward establishing trust in adaptive agents. In: Proceedings of the 13th International Conference on Intelligent User Interfaces, pp. 227–236 (2008)
Guidotti, R., Monreale, A., Ruggieri, S., Turini, F., Giannotti, F., Pedreschi, D.: A survey of methods for explaining black box models. ACM Comput. Surv. (CSUR) 51(5), 1–42 (2018)
Haarnoja, T., Zhou, A., Abbeel, P., Levine, S.: Soft actor-critic: off-policy maximum entropy deep reinforcement learning with a stochastic actor. In: International Conference on Machine Learning, pp. 1861–1870, PMLR (2018)
Hein, D., Udluft, S., Runkler, T.A.: Interpretable policies for reinforcement learning by genetic programming. Eng. Appl. Artif. Intell. 76, 158–169 (2018)
Henderson, P., Islam, R., Bachman, P., Pineau, J., Precup, D., Meger, D.: Deep reinforcement learning that matters. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 32 (2018)
Kantschik, W., Banzhaf, W.: Linear-graph GP - a new GP structure. In: Foster, J.A., Lutton, E., Miller, J., Ryan, C., Tettamanzi, A. (eds.) EuroGP 2002. LNCS, vol. 2278, pp. 83–92. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45984-7_8
Kaufmann, E., Bauersfeld, L., Loquercio, A., Müller, M., Koltun, V., Scaramuzza, D.: Champion-level drone racing using deep reinforcement learning. Nature 620(7976), 982–987 (2023)
Kelly, S., Heywood, M.I.: Emergent tangled graph representations for Atari game playing agents. In: McDermott, J., Castelli, M., Sekanina, L., Haasdijk, E., García-Sánchez, P. (eds.) EuroGP 2017. LNCS, vol. 10196, pp. 64–79. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-55696-3_5
Kelly, S., Heywood, M.I.: Multi-task learning in atari video games with emergent tangled program graphs. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 195–202 (2017)
Kelly, S., et al.: Discovering adaptable symbolic algorithms from scratch. arXiv preprint arXiv:2307.16890 (2023)
Kelly, S., Voegerl, T., Banzhaf, W., Gondro, C.: Evolving hierarchical memory-prediction machines in multi-task reinforcement learning. Genet. Program Evolvable Mach. 22, 573–605 (2021)
Koza, J.R.: Genetic programming as a means for programming computers by natural selection. Stat. Comput. 4(2), 87–112 (1994)
Koza, J.R., Rice, J.P.: Automatic programming of robots using genetic programming. In: AAAI, vol. 92, pp. 194–207 (1992)
Landajuela, M., et al.: Discovering symbolic policies with deep reinforcement learning. In: International Conference on Machine Learning, pp. 5979–5989, PMLR (2021)
Lipton, Z.C.: The mythos of model interpretability: in machine learning, the concept of interpretability is both important and slippery. Queue 16(3), 31–57 (2018)
Liu, D., Virgolin, M., Alderliesten, T., Bosman, P.A.: Evolvability degeneration in multi-objective genetic programming for symbolic regression. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 973–981 (2022)
Machado, M.C., Bellemare, M.G., Talvitie, E., Veness, J., Hausknecht, M., Bowling, M.: Revisiting the arcade learning environment: evaluation protocols and open problems for general agents. J. Artif. Intell. Res. 61, 523–562 (2018)
Medvet, E., Nadizar, G.: GP for continuous control: teacher or learner? The case of simulated modular soft robots. In: Winkler, S., Trujillo, L., Ofria, C., Hu, T. (eds.) Genetic Programming Theory and Practice XX. Genetic and Evolutionary Computation, Springer, Singapore (2023). https://doi.org/10.1007/978-981-99-8413-8_11
Miller, J.F.: Cartesian genetic programming: its status and future. Genet. Program Evolvable Mach. 21, 129–168 (2020)
Miller, J.F., Thomson, P.: Cartesian genetic programming. In: Poli, R., Banzhaf, W., Langdon, W.B., Miller, J., Nordin, P., Fogarty, T.C. (eds.) EuroGP 2000. LNCS, vol. 1802, pp. 121–132. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-540-46239-2_9
Nadizar, G., Rovito, L., De Lorenzo, A., Medvet, E., Virgolin, M.: An analysis of the ingredients for learning interpretable symbolic regression models with human-in-the-loop and genetic programming. ACM Tran. Evol. Learn. (2024)
Puiutta, E., Veith, E.M.S.P.: Explainable reinforcement learning: a survey. In: Holzinger, A., Kieseberg, P., Tjoa, A.M., Weippl, E. (eds.) CD-MAKE 2020. LNCS, vol. 12279, pp. 77–95. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-57321-8_5
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (2014)
Rudin, C.: Stop explaining black box machine learning models for high stakes decisions and use interpretable models instead. Nat. Mach. Intell. 1(5), 206–215 (2019)
Salvato, E., Fenu, G., Medvet, E., Pellegrino, F.A.: Crossing the reality gap: a survey on sim-to-real transferability of robot controllers in reinforcement learning. IEEE Access 9, 153171–153187 (2021)
Schulman, J., Wolski, F., Dhariwal, P., Radford, A., Klimov, O.: Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347 (2017)
Sigaud, O., Stulp, F.: Policy search in continuous action domains: an overview. Neural Netw. 113, 28–40 (2019)
Silver, D., et al.: Mastering the game of go with deep neural networks and tree search. Nature 529(7587), 484–489 (2016)
Todorov, E., Erez, T., Tassa, Y.: Mujoco: a physics engine for model-based control. In: 2012 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 5026–5033. IEEE (2012)
Verma, A., Murali, V., Singh, R., Kohli, P., Chaudhuri, S.: Programmatically interpretable reinforcement learning. In: International Conference on Machine Learning, pp. 5045–5054. PMLR (2018)
Videau, M., Leite, A., Teytaud, O., Schoenauer, M.: Multi-objective genetic programming for explainable reinforcement learning. In: Medvet, E., Pappa, G., Xue, B. (eds.) EuroGP 2022. LNCS, vol. 13223, pp. 278–293. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-02056-8_18
Virgolin, M., De Lorenzo, A., Medvet, E., Randone, F.: Learning a formula of interpretability to learn interpretable formulas. In: Bäck, T., et al. (eds.) PPSN 2020. LNCS, vol. 12270, pp. 79–93. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-58115-2_6
Virgolin, M., De Lorenzo, A., Randone, F., Medvet, E., Wahde, M.: Model learning with personalized interpretability estimation (ml-pie). In: Proceedings of the Genetic and Evolutionary Computation Conference Companion, pp. 1355–1364 (2021)
Wells, L., Bednarz, T.: Explainable AI and reinforcement learning-a systematic review of current approaches and trends. Front. Artif. Intell. 4, 550030 (2021)
Wilson, D.G., Cussat-Blanc, S., Luga, H., Miller, J.F.: Evolving simple programs for playing Atari games. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 229–236 (2018)
Wilson, D.G., Miller, J.F., Cussat-Blanc, S., Luga, H.: Positional cartesian genetic programming. arXiv preprint arXiv:1810.04119 (2018)
Zhou, R., Hu, T.: Evolutionary approaches to explainable machine learning. arXiv preprint arXiv:2306.14786 (2023)
Acknowledgements
The paper is based upon work from a scholarship supported by SPECIES (http://species-society.org), the Society for the Promotion of Evolutionary Computation in Europe and its Surroundings. This study was carried out within the PNRR research activities of the consortium iNEST (Interconnected North-Est Innovation Ecosystem) funded by the European Union Next-GenerationEU (Piano Nazionale di Ripresa e Resilienza (PNRR) - Missione 4 Componente 2, Investimento 1.5 - D.D. 1058 23/06/2022, ECS_00000043).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Nadizar, G., Medvet, E., Wilson, D.G. (2024). Naturally Interpretable Control Policies via Graph-Based Genetic Programming. In: Giacobini, M., Xue, B., Manzoni, L. (eds) Genetic Programming. EuroGP 2024. Lecture Notes in Computer Science, vol 14631. Springer, Cham. https://doi.org/10.1007/978-3-031-56957-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-031-56957-9_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-56956-2
Online ISBN: 978-3-031-56957-9
eBook Packages: Computer ScienceComputer Science (R0)