# Reinforcement Learning Library: pyqlearning `pyqlearning` is Python library to implement Reinforcement Learning and Deep Reinforcement Learning, especially for Q-Learning, Deep Q-Network, and Multi-agent Deep Q-Network which can be optimized by Annealing models such as Simulated Annealing, Adaptive Simulated Annealing, and Quantum Monte Carlo Method. This library makes it possible to design the information search algorithm such as the Game AI, web crawlers, or Robotics. But this library provides components for designers, not for end-users of state-of-the-art black boxes. Briefly speaking the philosophy of this library, *give user hype-driven blackboxes and you feed him for a day; show him how to design algorithms and you feed him for a lifetime.* So algorithm is power.
Deep Reinforcement Learning (Deep Q-Network: DQN) to solve Maze. |
Multi-agent Deep Reinforcement Learning to solve the pursuit-evasion game. |
Egorov, M. (2016). Multi-agent deep reinforcement learning., p4.
An important aspect of this data modeling is that by expressing each state of the multi-agent as channels, it is possible to enclose states of all the agents as **a target of convolution operation all at once**. By the affine transformation executed by the neural network, combinations of an enormous number of states of multi-agent can be computed in principle with an allowable range of memory.Egorov, M. (2016). Multi-agent deep reinforcement learning., p4.
[demo/multi_agent_maze_by_deep_q_network.ipynb](https://github.com/accel-brain/accel-brain-code/blob/master/Reinforcement-Learning/demo/multi_agent_maze_by_deep_q_network.ipynb) also prototypes Multi Agent Deep Q-Network to solve the pursuit-evasion game based on the image-like state representation of the multi-agent. * Black squares represent a wall. * Light gray squares represent passages. * A dark gray square represents a start point. * Moving dark gray squares represent enemies. * A white squeare represents a goal point. ## Tutorial: Complexity of Hyperparameters, or how can be hyperparameters decided? There are many hyperparameters that we have to set before the actual searching and learning process begins. Each parameter should be decided in relation to Deep/Reinforcement Learning theory and it cause side effects in training model. Because of this complexity of hyperparameters, so-called the hyperparameter tuning must become a burden of Data scientists and R & D engineers from the perspective of not only a theoretical point of view but also implementation level. ### Combinatorial optimization problem and Simulated Annealing. This issue can be considered as **Combinatorial optimization problem** which is an optimization problem, where an optimal solution has to be identified from a finite set of solutions. The solutions are normally discrete or can be converted into discrete. This is an important topic studied in operations research such as software engineering, artificial intelligence(AI), and machine learning. For instance, travelling sales man problem is one of the popular combinatorial optimization problem. In this problem setting, this library provides an Annealing Model to search optimal combination of hyperparameters. For instance, **Simulated Annealing** is a probabilistic single solution based search method inspired by the annealing process in metallurgy. Annealing is a physical process referred to as tempering certain alloys of metal, glass, or crystal by heating above its melting point, holding its temperature, and then cooling it very slowly until it solidifies into a perfect crystalline structure. The simulation of this process is known as simulated annealing. ### Functional comparison. [demo/annealing_hand_written_digits.ipynb](https://github.com/chimera0/accel-brain-code/blob/master/Reinforcement-Learning/demo/annealing_hand_written_digits.ipynb) is a Jupyter notebook which demonstrates a very simple classification problem: Recognizing hand-written digits, in which the aim is to assign each input vector to one of a finite number of discrete categories, to learn observed data points from already labeled data how to predict the class of unlabeled data. In the usecase of hand-written digits dataset, the task is to predict, given an image, which digit it represents. There are many structural extensions and functional equivalents of **Simulated Annealing**. For instance, **Adaptive Simulated Annealing**, also known as the very fast simulated reannealing, is a very efficient version of simulated annealing. And **Quantum Monte Carlo**, which is generally known a stochastic method to solve the Schrödinger equation, is one of the earliest types of solution in order to simulate the **Quantum Annealing** in classical computer. In summary, one of the function of this algorithm is to solve the ground state search problem which is known as logically equivalent to combinatorial optimization problem. Then this Jupyter notebook demonstrates functional comparison in the same problem setting. ## Demonstration: Epsilon Greedy Q-Learning and Simulated Annealing. Import python modules. ```python from pyqlearning.annealingmodel.costfunctionable.greedy_q_learning_cost import GreedyQLearningCost from pyqlearning.annealingmodel.simulated_annealing import SimulatedAnnealing # See demo/demo_maze_greedy_q_learning.py from demo.demo_maze_greedy_q_learning import MazeGreedyQLearning ``` The class `GreedyQLearningCost` is implemented the interface `CostFunctionable` to be called by `AnnealingModel`. This cost function is defined by where is the number of searching(learning) and L is a limit of . Like Monte Carlo method, let us draw random samples from a normal (Gaussian) or unifrom distribution. ```python # Epsilon-Greedy rate in Epsilon-Greedy-Q-Learning. greedy_rate_arr = np.random.normal(loc=0.5, scale=0.1, size=100) # Alpha value in Q-Learning. alpha_value_arr = np.random.normal(loc=0.5, scale=0.1, size=100) # Gamma value in Q-Learning. gamma_value_arr = np.random.normal(loc=0.5, scale=0.1, size=100) # Limit of the number of Learning(searching). limit_arr = np.random.normal(loc=10, scale=1, size=100) var_arr = np.c_[greedy_rate_arr, alpha_value_arr, gamma_value_arr, limit_arr] ``` Instantiate and initialize `MazeGreedyQLearning` which is-a `GreedyQLearning`. ```python # Instantiation. greedy_q_learning = MazeGreedyQLearning() greedy_q_learning.initialize(hoge=fuga) ``` Instantiate `GreedyQLearningCost` which is implemented the interface `CostFunctionable` to be called by `AnnealingModel`. ```python init_state_key = ("Some", "data") cost_functionable = GreedyQLearningCost( greedy_q_learning, init_state_key=init_state_key ) ``` Instantiate `SimulatedAnnealing` which is-a `AnnealingModel`. ```python annealing_model = SimulatedAnnealing( # is-a `CostFunctionable`. cost_functionable=cost_functionable, # The number of annealing cycles. cycles_num=5, # The number of trials of searching per a cycle. trials_per_cycle=3 ) ``` Fit the `var_arr` to `annealing_model`. ```python annealing_model.var_arr = var_arr ``` Start annealing. ```python annealing_model.annealing() ``` To extract result of searching, call the property `predicted_log_list` which is list of tuple: `(Cost, Delta energy, Mean of delta energy, probability in Boltzmann distribution, accept flag)`. And refer the property `x` which is `np.ndarray` that has combination of hyperparameters. The optimal combination can be extracted as follow. ```python # Extract list: [(Cost, Delta energy, Mean of delta energy, probability, accept)] predicted_log_arr = annealing_model.predicted_log_arr # [greedy rate, Alpha value, Gamma value, Limit of the number of searching.] min_e_v_arr = annealing_model.var_arr[np.argmin(predicted_log_arr[:, 2])] ``` ### Contingency of definitions The above definition of cost function is possible option: not necessity but contingent from the point of view of modal logic. You should questions the necessity of definition and re-define, for designing the implementation of interface `CostFunctionable`, in relation to *your* problem settings. ## Demonstration: Epsilon Greedy Q-Learning and Adaptive Simulated Annealing. There are various Simulated Annealing such as Boltzmann Annealing, Adaptive Simulated Annealing(SAS), and Quantum Simulated Annealing. On the premise of Combinatorial optimization problem, these annealing methods can be considered as functionally equivalent. The *Commonality/Variability* in these methods are able to keep responsibility of objects all straight as the class diagram below indicates. ### Code sample. `AdaptiveSimulatedAnnealing` is-a subclass of `SimulatedAnnealing`. The *variability* is aggregated in the method `AdaptiveSimulatedAnnealing.adaptive_set()` which must be called before executing `AdaptiveSimulatedAnnealing.annealing()`. ```python from pyqlearning.annealingmodel.simulatedannealing.adaptive_simulated_annealing import AdaptiveSimulatedAnnealing annealing_model = AdaptiveSimulatedAnnealing( cost_functionable=cost_functionable, cycles_num=33, trials_per_cycle=3, accepted_sol_num=0.0, init_prob=0.7, final_prob=0.001, start_pos=0, move_range=3 ) # Variability part. annealing_model.adaptive_set( # How often will this model reanneals there per cycles. reannealing_per=50, # Thermostat. thermostat=0., # The minimum temperature. t_min=0.001, # The default temperature. t_default=1.0 ) annealing_model.var_arr = params_arr annealing_model.annealing() ``` To extract result of searching, call the property like the case of using `SimulatedAnnealing`. If you want to know how to visualize the searching process, see my Jupyter notebook: [demo/annealing_hand_written_digits.ipynb](https://github.com/chimera0/accel-brain-code/blob/master/Reinforcement-Learning/demo/annealing_hand_written_digits.ipynb). ## Demonstration: Epsilon Greedy Q-Learning and Quantum Monte Carlo. Generally, Quantum Monte Carlo is a stochastic method to solve the Schrödinger equation. This algorithm is one of the earliest types of solution in order to simulate the Quantum Annealing in classical computer. In summary, one of the function of this algorithm is to solve the ground state search problem which is known as logically equivalent to combinatorial optimization problem. According to theory of spin glasses, the ground state search problem can be described as minimization energy determined by the hamiltonian as follow where refers to the Pauli spin matrix below for the spin-half particle at lattice point . In spin glasses, random value is assigned to . The number of combinations is enormous. If this value is , a trial frequency is . This computation complexity makes it impossible to solve the ground state search problem. Then, in theory of spin glasses, the standard hamiltonian is re-described in expanded form. where also refers to the Pauli spin matrix and is so-called annealing coefficient, which is hyperparameter that contains vely high value. Ising model to follow this Hamiltonian is known as the Transverse Ising model. In relation to this system, thermal equilibrium amount of a physical quantity is as follow. If is a diagonal matrix, then also is diagonal matrix. If diagonal element in is , Each diagonal element is . However if has off-diagonal elements, It is known that since for any of the exponent we must exponentiate the matrix as follow. Therefore, a path integration based on Trotter-Suzuki decomposition has been introduced in Quantum Monte Carlo Method. This path integration makes it possible to obtain the partition function . where if is large enough, relational expression below is established. Then the partition function can be re-descibed as follow. where is topological products (product spaces). Because is the diagonal matrix, . Therefore, The partition function can be re-descibed as follow. where is the number of trotter. This relational expression indicates that the quantum - mechanical Hamiltonian in dimentional Tranverse Ising model is functional equivalence to classical Hamiltonian in dimentional Ising model, which means that the state of the quantum - mechanical system can be approximate by the state of classical system. ### Code sample. ```python from pyqlearning.annealingmodel.quantum_monte_carlo import QuantumMonteCarlo from pyqlearning.annealingmodel.distancecomputable.cost_as_distance import CostAsDistance # User defined function which is-a `CostFuntionable`. cost_functionable = YourCostFunctions() # Compute cost as distance for `QuantumMonteCarlo`. distance_computable = CostAsDistance(params_arr, cost_functionable) # Init. annealing_model = QuantumMonteCarlo( distance_computable=distance_computable, # The number of annealing cycles. cycles_num=100, # Inverse temperature (Beta). inverse_temperature_beta=0.1, # Gamma. (so-called annealing coefficient.) gammma=1.0, # Attenuation rate for simulated time. fractional_reduction=0.99, # The dimention of Trotter. trotter_dimention=10, # The number of Monte Carlo steps. mc_step=100, # The number of parameters which can be optimized. point_num=100, # Default `np.ndarray` of 2-D spin glass in Ising model. spin_arr=None, # Tolerance for the optimization. # When the ΔE is not improving by at least `tolerance_diff_e` # for two consecutive iterations, annealing will stops. tolerance_diff_e=0.01 ) # Execute annealing. annealing_model.annealing() ``` To extract result of searching, call the property like the case of using `SimulatedAnnealing`. If you want to know how to visualize the searching process, see my Jupyter notebook: [demo/annealing_hand_written_digits.ipynb](https://github.com/chimera0/accel-brain-code/blob/master/Reinforcement-Learning/demo/annealing_hand_written_digits.ipynb). ## References ### Q-Learning models. - Agrawal, S., & Goyal, N. (2011). Analysis of Thompson sampling for the multi-armed bandit problem. arXiv preprint arXiv:1111.1797. - Bubeck, S., & Cesa-Bianchi, N. (2012). Regret analysis of stochastic and nonstochastic multi-armed bandit problems. arXiv preprint arXiv:1204.5721. - Chapelle, O., & Li, L. (2011). An empirical evaluation of thompson sampling. In Advances in neural information processing systems (pp. 2249-2257). - Du, K. L., & Swamy, M. N. S. (2016). Search and optimization by metaheuristics (p. 434). New York City: Springer. - Kaufmann, E., Cappe, O., & Garivier, A. (2012). On Bayesian upper confidence bounds for bandit problems. In International Conference on Artificial Intelligence and Statistics (pp. 592-600). - Mnih, V., Kavukcuoglu, K., Silver, D., Graves, A., Antonoglou, I., Wierstra, D., & Riedmiller, M. (2013). Playing atari with deep reinforcement learning. arXiv preprint arXiv:1312.5602. - Richard Sutton and Andrew Barto (1998). Reinforcement Learning. MIT Press. - Watkins, C. J. C. H. (1989). Learning from delayed rewards (Doctoral dissertation, University of Cambridge). - Watkins, C. J., & Dayan, P. (1992). Q-learning. Machine learning, 8(3-4), 279-292. - White, J. (2012). Bandit algorithms for website optimization. ” O’Reilly Media, Inc.”. ### Deep Q-Network models. - Cho, K., Van Merriënboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., & Bengio, Y. (2014). Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv preprint arXiv:1406.1078. - Egorov, M. (2016). Multi-agent deep reinforcement learning. - Gupta, J. K., Egorov, M., & Kochenderfer, M. (2017, May). Cooperative multi-agent control using deep reinforcement learning. In International Conference on Autonomous Agents and Multiagent Systems (pp. 66-83). Springer, Cham. - Malhotra, P., Ramakrishnan, A., Anand, G., Vig, L., Agarwal, P., & Shroff, G. (2016). LSTM-based encoder-decoder for multi-sensor anomaly detection. arXiv preprint arXiv:1607.00148. - Mnih, V., Kavukcuoglu, K., Silver, D., Graves, A., Antonoglou, I., Wierstra, D., & Riedmiller, M. (2013). Playing atari with deep reinforcement learning. arXiv preprint arXiv:1312.5602. - Sainath, T. N., Vinyals, O., Senior, A., & Sak, H. (2015, April). Convolutional, long short-term memory, fully connected deep neural networks. In Acoustics, Speech and Signal Processing (ICASSP), 2015 IEEE International Conference on (pp. 4580-4584). IEEE. - Xingjian, S. H. I., Chen, Z., Wang, H., Yeung, D. Y., Wong, W. K., & Woo, W. C. (2015). Convolutional LSTM network: A machine learning approach for precipitation nowcasting. In Advances in neural information processing systems (pp. 802-810). - Zaremba, W., Sutskever, I., & Vinyals, O. (2014). Recurrent neural network regularization. arXiv preprint arXiv:1409.2329. ### Annealing models. - Bektas, T. (2006). The multiple traveling salesman problem: an overview of formulations and solution procedures. Omega, 34(3), 209-219. - Bertsimas, D., & Tsitsiklis, J. (1993). Simulated annealing. Statistical science, 8(1), 10-15. - Das, A., & Chakrabarti, B. K. (Eds.). (2005). Quantum annealing and related optimization methods (Vol. 679). Springer Science & Business Media. - Du, K. L., & Swamy, M. N. S. (2016). Search and optimization by metaheuristics. New York City: Springer. - Edwards, S. F., & Anderson, P. W. (1975). Theory of spin glasses. Journal of Physics F: Metal Physics, 5(5), 965. - Facchi, P., & Pascazio, S. (2008). Quantum Zeno dynamics: mathematical and physical aspects. Journal of Physics A: Mathematical and Theoretical, 41(49), 493001. - Heim, B., Rønnow, T. F., Isakov, S. V., & Troyer, M. (2015). Quantum versus classical annealing of Ising spin glasses. Science, 348(6231), 215-217. - Heisenberg, W. (1925) Über quantentheoretische Umdeutung kinematischer und mechanischer Beziehungen. Z. Phys. 33, pp.879—893. - Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift fur Physik, 43, 172-198. - Heisenberg, W. (1984). The development of quantum mechanics. In Scientific Review Papers, Talks, and Books -Wissenschaftliche Übersichtsartikel, Vorträge und Bücher (pp. 226-237). Springer Berlin Heidelberg. Hilgevoord, Jan and Uffink, Jos, "The Uncertainty Principle", The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2016/entries/qt-uncertainty/>. - Jarzynski, C. (1997). Nonequilibrium equality for free energy differences. Physical Review Letters, 78(14), 2690. - Messiah, A. (1966). Quantum mechanics. 2 (1966). North-Holland Publishing Company. - Mezard, M., & Montanari, A. (2009). Information, physics, and computation. Oxford University Press. - Nallusamy, R., Duraiswamy, K., Dhanalaksmi, R., & Parthiban, P. (2009). Optimization of non-linear multiple traveling salesman problem using k-means clustering, shrink wrap algorithm and meta-heuristics. International Journal of Nonlinear Science, 8(4), 480-487. - Schrödinger, E. (1926). Quantisierung als eigenwertproblem. Annalen der physik, 385(13), S.437-490. - Somma, R. D., Batista, C. D., & Ortiz, G. (2007). Quantum approach to classical statistical mechanics. Physical review letters, 99(3), 030603. - 鈴木正. (2008). 「組み合わせ最適化問題と量子アニーリング: 量子断熱発展の理論と性能評価」.,『物性研究』, 90(4): pp598-676. 参照箇所はpp619-624. - 西森秀稔、大関真之(2018) 『量子アニーリングの基礎』須藤 彰三、岡 真 監修、共立出版、参照箇所はpp9-46. ### More detail demos - [Webクローラ型人工知能:キメラ・ネットワークの仕様](https://media.accel-brain.com/_chimera-network-is-web-crawling-ai/) (Japanese) - 20001 bots are running as 20001 web-crawlers and 20001 web-scrapers. - [ロボアドバイザー型人工知能:キメラ・ネットワークの仕様](https://media.accel-brain.com/_chimera-network-is-robo-adviser/) (Japanese) - The 20001 bots can also simulate the portfolio optimization of securities such as stocks and circulation currency such as cryptocurrencies. ### Related PoC - [量子力学、統計力学、熱力学における天才物理学者たちの神学的な形象について](https://accel-brain.com/das-theologische-bild-genialer-physiker-in-der-quantenmechanik-und-der-statistischen-mechanik-und-thermodynamik/) (Japanese) - [熱力学の前史、マクスウェル=ボルツマン分布におけるエントロピーの歴史的意味論](https://accel-brain.com/das-theologische-bild-genialer-physiker-in-der-quantenmechanik-und-der-statistischen-mechanik-und-thermodynamik/historische-semantik-der-entropie-in-der-maxwell-boltzmann-verteilung/) - [メディアとしての統計力学と形式としてのアンサンブル、そのギブス的類推](https://accel-brain.com/das-theologische-bild-genialer-physiker-in-der-quantenmechanik-und-der-statistischen-mechanik-und-thermodynamik/statistische-mechanik-als-medium-und-ensemble-als-form/) - [「マクスウェルの悪魔」、力学の基礎法則としての神](https://accel-brain.com/das-theologische-bild-genialer-physiker-in-der-quantenmechanik-und-der-statistischen-mechanik-und-thermodynamik/maxwell-damon/) - [Webクローラ型人工知能によるパラドックス探索暴露機能の社会進化論](https://accel-brain.com/social-evolution-of-exploration-and-exposure-of-paradox-by-web-crawling-type-artificial-intelligence/) (Japanese) - [World-Wide Webの社会構造とWebクローラ型人工知能の意味論](https://accel-brain.com/social-evolution-of-exploration-and-exposure-of-paradox-by-web-crawling-type-artificial-intelligence/sozialstruktur-des-world-wide-web-und-semantik-der-kunstlichen-intelligenz-des-web-crawlers/) - [意味論の意味論、観察の観察](https://accel-brain.com/social-evolution-of-exploration-and-exposure-of-paradox-by-web-crawling-type-artificial-intelligence/semantik-der-semantik-und-beobachtung-der-beobachtung/) - [深層強化学習のベイズ主義的な情報探索に駆動された自然言語処理の意味論](https://accel-brain.com/semantics-of-natural-language-processing-driven-by-bayesian-information-search-by-deep-reinforcement-learning/) (Japanese) - [バンディットアルゴリズムの機能的拡張としての強化学習アルゴリズム](https://accel-brain.com/semantics-of-natural-language-processing-driven-by-bayesian-information-search-by-deep-reinforcement-learning/verstarkungslernalgorithmus-als-funktionale-erweiterung-des-banditenalgorithmus/) - [深層強化学習の統計的機械学習、強化学習の関数近似器としての深層学習](https://accel-brain.com/semantics-of-natural-language-processing-driven-by-bayesian-information-search-by-deep-reinforcement-learning/deep-learning-als-funktionsapproximator-fur-verstarktes-lernen/) - [ハッカー倫理に準拠した人工知能のアーキテクチャ設計](https://accel-brain.com/architectural-design-of-artificial-intelligence-conforming-to-hacker-ethics/) (Japanese) - [アーキテクチャ中心設計の社会構造とアーキテクチャの意味論](https://accel-brain.com/architectural-design-of-artificial-intelligence-conforming-to-hacker-ethics/sozialstruktur-des-architekturzentrum-designs-und-architektur-der-semantik/) - [「人工の理想」を背景とした「万物照応」のデータモデリング](https://accel-brain.com/data-modeling-von-korrespondenz-in-artificial-paradise/) (Japanese) - [ギャンブラーの機能的等価物としての強化学習エージェント、投資における冷静沈着な精神の現在性](https://accel-brain.com/data-modeling-von-korrespondenz-in-artificial-paradise/agent-in-reignforcement-lernen-als-funktionelle-aquivalente-von-spielern/) ## Author - accel-brain ## Author URI - https://accel-brain.co.jp/ - https://accel-brain.com/ ## License - GNU General Public License v2.0