Evaluate the gradient using the below expression: 4. The REINFORCE Algorithm aka Monte-Carlo Policy Differentiation The setup for the general reinforcement learning problem is as follows. Represents a key derivation algorithm provider. In this post, weâll look at the REINFORCE algorithm and test it using OpenAIâs CartPole environment with PyTorch. Find the full implementation and write-up on https://github.com/thechrisyoon08/Reinforcement-Learning! Namespace: Windows.Security.Cryptography.Core. the sum of rewards in a trajectory(we are just considering finite undiscounted horizon). Now we can rewrite our gradient as below: We can derive this equation as follows[6][7][9]: Probability of trajectory with respect to parameter θ, P(τ|θ) can be expanded as follows[6][7]: Where p(s0) is the probability distribution of starting state and P(st+1|st, at) is the transition probability of reaching new state st+1 by performing the action at from the state st. The left-hand side of the equation can be replaced as below: REINFORCE is the Mote-Carlo sampling of policy gradient methods. If we take the log-probability of the trajectory, then it can be derived as below[7]: We can take the gradient of the log-probability of a trajectory thus gives[6][7]: We can modify this function as shown below based on the transition probability model, P(st+1∣st, at) disappears because we are considering the model-free policy gradient algorithm where the transition probability model is not necessary. algorithm to find derivative. A2A. It is important to understand a few concepts in RL before we get into the policy gradient. I'm looking at Sutton & Barto's rendition of the REINFORCE algorithm (from their book here, pg. This type of algorithms is model-free reinforcement learning(RL). Put simply: random forest builds multiple decision trees and merges them together to get a more accurate and stable prediction. In the future, more algorithms will be added and the existing codes will also be maintained. A simple implementation of this algorithm would involve creating a Policy: a model that takes a state as input â¦ REINFORCE is a Monte-Carlo variant of policy gradients (Monte-Carlo: taking random samples). If a take the following example : Action #1 give a low reward (-1 for the example) Action #2 give a high reward (+1 for the example) This post assumes some familiarity in reinforcement learning! We're given an environment $\mathcal{E}$ with a specified state space $\mathcal{S}$ and an action space $\mathcal{A}$ giving the allowable actions in â¦ Frequently appearing in literature is the expectation notation â it is used because we want to optimize long term future (predicted) rewards, which has a degree of uncertainty. Mathematically you can also interpret these tricks as a way of controlling the variance of the policy gradient estimator. Reinforcement learning is probably the most general framework inwhich reward-related learning problems of animals, humans or machinecan be phrased. Chapter 11 T utorial: The Kalman Filter T on y Lacey. https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume4/kaelbling96a-html/node20.html, http://www.inf.ed.ac.uk/teaching/courses/rl/slides15/rl08.pdf, https://mc.ai/deriving-policy-gradients-and-implementing-reinforce/, http://rail.eecs.berkeley.edu/deeprlcourse-fa17/f17docs/lecture_4_policy_gradient.pdf, https://towardsdatascience.com/the-almighty-policy-gradient-in-reinforcement-learning-6790bee8db6, https://www.janisklaise.com/post/rl-policy-gradients/, https://spinningup.openai.com/en/latest/spinningup/rl_intro3.html#deriving-the-simplest-policy-gradient, https://www.rapidtables.com/math/probability/Expectation.html, https://karpathy.github.io/2016/05/31/rl/, https://lilianweng.github.io/lil-log/2018/02/19/a-long-peek-into-reinforcement-learning.html, http://machinelearningmechanic.com/deep_learning/reinforcement_learning/2019/12/06/a_mathematical_introduction_to_policy_gradient.html, https://www.wordstream.com/blog/ws/2017/07/28/machine-learning-applications, More from Intro to Artificial Intelligence, Camera-Lidar Projection: Navigating between 2D and 3D, Training an MLP from scratch using Backpropagation for solving Mathematical Equations, Simple Monte Carlo Options Pricer In Python, Processing data for Machine Learning with TensorFlow, When to use Reinforcement Learning (and when not to), CatBoost: Cross-Validated Bayesian Hyperparameter Tuning, Convolutional Neural Networks — Part 3: Convolutions Over Volume and the ConvNet Layer. From a mathematical perspective, an objective function is to minimise or maximise something. Infinite-horizon policy-gradient estimation: temporally decomposed policy gradient (not the first paper on this! What weâll call the REINFORCE algorithm was part of a family of algorithms first proposed by Ronald Williams in 1992. That means the RL agent sample from starting state to goal state directly from the environment, rather than bootstrapping compared to other methods such as Temporal Difference Learning and Dynamic programming. 2. The loss used in REINFORCE algorithm is confusing me. â¢Williams (1992). Running the main loop, we observe how the policy is learned over 5000 training episodes. This algorithm is the fundamental policy gradient algorithm on which nearly all the advanced policy gradient algorithms are based. We can define our return as the sum of rewards from the current state to the goal state i.e. With the y-axis representing the number of steps the agent balances the pole before letting it fall, we see that, over time, the agent learns to balance the pole for a longer duration. Andrej Kaparthyâs post: http://karpathy.github.io/2016/05/31/rl/, Official PyTorch implementation in https://github.com/pytorch/examples, Lecture slides from University of Toronto: http://www.cs.toronto.edu/~tingwuwang/REINFORCE.pdf, https://github.com/thechrisyoon08/Reinforcement-Learning, http://www.cs.toronto.edu/~tingwuwang/REINFORCE.pdf, https://www.linkedin.com/in/chris-yoon-75847418b/, Multi-task Learning and Calibration for Utility-based Home Feed Ranking, Unhappy Truckers and Other Algorithmic Problems, Estimating Vegetated Surfaces with Computer Vision: how we improved our model and scaled up, Perform a trajectory roll-out using the current policy, Store log probabilities (of policy) and reward values at each step, Calculate discounted cumulative future reward at each step, Compute policy gradient and update policy parameter. The "forest" it builds, is an ensemble of decision trees, usually trained with the âbaggingâ method. subtract mean, divide by standard deviation) before we plug them into backprop. In deriving the most basic policy gradiant algorithm, REINFORCE, we seek the optimal policy that will maximize the total expected reward: where The trajectory is a sequence of states and actions experienced by the agent, is the return , and is the probability of observing that particular sequence of states and actions. When p 0 and Rare not known, one can replace the Bellman equation by a sampling variant J Ë(x) = J Ë(x)+ (r+ J Ë(x0) J Ë(x)): (2) with xthe current state of the agent, x0the new state after choosing action u from Ë(ujx) and rthe actual observed reward. Gradient descent requires access to the gradient of the loss function with respect to all the weights in the network to perform a weight update, in order to minimize the loss function. In this article public ref class KeyDerivationAlgorithmProvider sealed 11.1 In tro duction The Kalman lter [1] has long b een regarded as the optimal solution to man y trac REINFORCE: A First Policy Gradient Algorithm. The goal of any Reinforcement Learning(RL) algorithm is to determine the optimal policy that has a maximum reward. In essence, policy gradient methods update the probability distribution of actions so that actions with higher expected reward have a higher probability value for an observed state. Policy gradient methods are ubiquitous in model free reinforcement learning algorithms â they appear frequently in reinforcement learning algorithms, especially so in recent publications. The policy gradient method is also the âactorâ part of Actor-Critic methods (check out my post on Actor Critic Methods), so understanding it is foundational to studying reinforcement learning! policy is a distribution over actions given states. We are now going to solve the CartPole-v0 environment using REINFORCE with normalized rewards*! Where P(x) represents the probability of the occurrence of random variable x, and f(x)is a function denoting the value of x. Since this is a maximization problem, we optimize the policy by taking the gradient ascent with the partial derivative of the objective with respect to the policy parameter theta. see actor-critic section later) â¢Peters & Schaal (2008). Please let me know if there are errors in the derivation! In the draft for Sutton's latest RL book, page 270, he derives the REINFORCE algorithm from the policy gradient theorem. This way weâre always encouraging and discouraging roughly half of the performed actions. Random forest is a supervised learning algorithm. The expectation, also known as the expected value or the mean, is computed by the summation of the product of every x value and its probability. REINFORCE is a Monte-Carlo variant of policy gradients (Monte-Carlo: taking random samples). The general idea of the bagging method is that a combination of learning models increases the overall result. The REINFORCE algorithm for policy-gradient reinforcement learning is a simple stochastic gradient algorithm. The gradient update rule is as shown below: The expectation of a discrete random variable X can be defined as: where x is the value of random variable X and P(x) is the probability function of x. Derivation: Assume that a circle is passing through origin and itâs radius is r . We can maximise the objective function J to maximises the return by adjusting the policy parameter θ to get the best policy. From Pytorch documentation: loss = -m.log_prob(action) * reward We want to minimize this loss. The gradient ascent is the optimisation algorithm that iteratively searches for optimal parameters that maximise the objective function. Thus,those systems need to be modeled as partially observableMarkov decision problems which oftenresults in exâ¦ Your derivation of the gradient seems correct to me. In Backward Algorithm we need to find the probability that the machine will be in hidden state \( s_i \) at time step t and will generate the remaining part of the sequence of the visible symbol \(V^T\). In policy gradient, the policy is usually modelled with a parameterized function respect to θ, πθ(a|s). Instead of a sampled/bootstrapped value function (as in Actor-Critic) or sampled full return (in REINFORCE) you can use the sampled reward. The REINFORCE algorithm is a direct differentiation of the reinforcement learning objective. 2. Value-function methods are better for longer episodes because they can start learning before the end of a â¦ By the end of this course, you should be able to: 1. To introduce this idea we will start with a simple policy gradient method called REINFORCE algorithm ( original paper). The policy function is parameterized by a neural network (since we live in the world of deep learning). A more in-depth exploration can be found here.â. Here, we will use the length of the episode as a performance index; longer episodes mean that the agent balanced the inverted pendulum for a longer time, which is what we want to see. In other words, we do not know the environment dynamics or transition probability. I'm writing program in Python and I need to find the derivative of a function (a function expressed as string). Deep Reinforcement Learning Algorithms This repository will implement the classic deep reinforcement learning algorithms by using PyTorch. REINFORCE algorithm with discounted rewards â where does gamma^t in the update come from?Reinforcement learning: understanding this derivation of n-step Tree Backup algorithmWhy do we normalize the discounted rewards when doing policy gradient reinforcement learning?How can we use the current rewards as a system input in the RUN time when working with Deep Q learning?Does self â¦ *Notice that the discounted reward is normalized (i.e. Backpropagation is an algorithm used to train neural networks, used along with an optimization routine such as gradient descent. Please have a look this medium post for the explanation of a few key concepts in RL. REINFORCE: Mathematical definitions The environment dynamics or transition probability is indicated as below: It can be read the probability of reaching the next state st+1 by taking the action from the current state s. Sometimes transition probability is confused with policy. Policy gradient is an approach to solve reinforcement learning problems. What is the reinforcement learning objective, you may ask? If youâre not familiar with policy gradients, the algorithm, or the environment, Iâd recommend going back to that post before continuing on here as I cover all the details there for you. Policy gradient methods are policy iterative method that means modelling and optimising the policy directly. We can rewrite our policy gradient expression in the context of Monte-Carlo sampling. Policy gradient algorithm is a policy iteration approach where policy is directly manipulated to reach the optimal policy that maximises the expected return. Viewed 21k times 3. If we can find out the gradient ∇ of the objective function J, as shown below: Then, we can update the policy parameter θ(for simplicity, we are going to use θ instead of πθ), using the gradient ascent rule. (Î¸). We assume a basic understanding of reinforcement learning, so if you donât know what states, actions, environments and the like mean, check out some of the links to other articles here or the simple primer on the topic here. Key Derivation Algorithm Provider Class Definition. Ask Question Asked 10 years, 9 months ago. Here, we are going to derive the policy gradient step-by-step, and implement the REINFORCE algorithm, also known as Monte Carlo Policy Gradients. We can now go back to the expectation of our algorithm and time to replace the gradient of the log-probability of a trajectory with the derived equation above. subtract by mean and divide by the standard deviation of all rewards in the episode). In a previous post we examined two flavors of the REINFORCE algorithm applied to OpenAIâs CartPole environment and implemented the algorithms in TensorFlow. The aim of this repository is to provide clear code for people to learn the deep reinforcemen learning algorithms. This inapplicabilitymay result from problems with uncertain state information. Whereas, transition probability explains the dynamics of the environment which is not readily available in many practical applications. Sample N trajectories by following the policy πθ. Simple statistical gradient-following algorithms for connectionist reinforcement learning: introduces REINFORCE algorithm â¢Baxter & Bartlett (2001). TD( ) and Q-learning algorithms. The PanâTompkins algorithm is commonly used to detect QRS complexes in electrocardiographic signals ().The QRS complex represents the ventricular depolarization and the main spike visible in an ECG signal (see figure). Policy gradient methods are policy iterative method that means modelling andâ¦ Where N is the number of trajectories is for one gradient update[6]. Backpropagation computes these gradients in a systematic way. Derivation of Backward Algorithm: algorithm deep-learning deep-reinforcement-learning pytorch dqn policy-gradient sarsa resnet a3c reinforce sac alphago actor-critic trpo ppo a2c actor-critic-algorithm â¦ If you havenât looked into the field of reinforcement learning, please first read the section âA (Long) Peek into Reinforcement Learning » Key Conceptsâfor the problem definition and key concepts. Active 3 years, 3 months ago. 328).I can't quite understand why there is $\gamma^t$ on the last line. No need to understand the colored part. The best policy will always maximise the return. REINFORCE Algorithm. Here R(st, at) is defined as reward obtained at timestep t by performing an action at from the state st. We know the fact that R(st, at) can be represented as R(τ). 2. REINFORCE is the simplest policy gradient algorithm, it works by increasing the likelihood of performing good actions more than bad ones using the sum of rewards as weights multiplied by the gradient, if the actions taken by the were good, then the sum will be relatively large and vice versa, which is essentially a formulation of trial and error learning. REINFORCE belongs to a special class of Reinforcement Learning algorithms called Policy Gradient algorithms. The agent collects a trajectory Ï of one episode using its current policy, and uses it to update the policy parameter. However, most of the methods proposed in thereinforcement learning community are not yet applicable to manyproblems such as robotics, motor control, etc. Now the policy gradient expression is derived as. It works well when episodes are reasonably short so lots of episodes can be simulated. For example, suppose we compute [discounted cumulative reward] for all of the 20,000 actions in the batch of 100 Pong game rollouts above. The goal of any Reinforcement Learning(RL) algorithm is to determine the optimal policy that has a maximum reward. We will assume discrete (finite) action space and a stochastic (non-deterministic) policy for this post. One big advantage of random forest is that it can be useâ¦ The model-free indicates that there is no prior knowledge of the model of the environment. Reinforced Molecular Optimization with Neighborhood-Controlled Grammars Chencheng Xu, 1,2Qiao Liu,1,3 Minlie Huang, Tao Jiang4,1,2 1BNRIST, Tsinghua University, Beijing 100084, China 2Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China 3Department of Automation, Tsinghua University, Beijing 100084, China 4Department of Computer Science and â¦ This provides stability in training, and is explained further in Andrej Kaparthyâs post: âIn practice it can can also be important to normalize these. d Ï ( s) = â k = 0 â Î³ k P ( S k = s | S 0, Ï) This way, we can update the parameters θ in the direction of the gradient(Remember the gradient gives the direction of the maximum change, and the magnitude indicates the maximum rate of change ). In other words, the policy defines the behaviour of the agent. Edit. If you like my write up, follow me on Github, Linkedin, and/or Medium profile. We start with the following derivation: âÎ¸EÏâ¼P Î¸ [f(Ï)] = âÎ¸ â« PÎ¸(Ï)f(Ï)dÏ = â« âÎ¸(PÎ¸(Ï)f(Ï))dÏ (swap integration with gradient) = â« (âÎ¸PÎ¸(Ï))f(Ï)dÏ (becaue f does not depend on Î¸) = â« PÎ¸(Ï)(âÎ¸ logPÎ¸(Ï))f(Ï)dÏ (because âlogPÎ¸(Ï) = âPÎ¸(Ï) Backward Algorithm: Backward Algorithm is the time-reversed version of the Forward Algorithm. We consider a stochastic, parameterized policy πθ and aim to maximise the expected return using objective function J(πθ)[7]. In his original paper, he wasnât able to show that this algorithm converges to a local optimum, although he was quite confident it would. REINFORCE algorithm is an algorithm that is {discrete domain + continuous domain, policy-based, on-policy + off-policy, model-free, shown up in last year's final}. The agent collects a trajectory Ï of one episode using its â¦ â s d Ï ( s) â a q Ï ( s, a) â Ï ( a | s, Î¸) = E [ Î³ t â a q Ï ( S t, a) â Ï ( a | S t, Î¸)] where. Repeat 1 to 3 until we find the optimal policy πθ. The first part is the equivalence. One good idea is to âstandardizeâ these returns (e.g. Since one full trajectory must be completed to construct a sample space, REINFORCE is updated in an off-policy way. They say: [..] in the boxed algorithms we are giving the algorithms for the general discounted [return] case. The objective function for policy gradients is defined as: In other words, the objective is to learn a policy that maximizes the cumulative future reward to be received starting from any given time t until the terminal time T. Note that r_{t+1} is the reward received by performing action a_{t} at state s_{t} ; r_{t+1} = R(s_{t}, a_{t}) where R is the reward function. Also be maintained you like my write up, follow me on Github, Linkedin, and/or medium profile reasonably! A parameterized function respect to θ, πθ ( a|s ) idea of the REINFORCE algorithm applied to CartPole. Able to: 1 the main loop, we observe how the policy function to! 3 until we find the full implementation and write-up on https: //github.com/thechrisyoon08/Reinforcement-Learning current,. Algorithm is a Monte-Carlo variant of policy gradients ( Monte-Carlo: taking random samples ) algorithm â¢Baxter & (. Let me know if there are errors in the boxed algorithms we are giving the algorithms TensorFlow... Policy gradient ( not the first paper on this current policy, and uses it to update the function. Inwhich reward-related learning problems of animals, humans or machinecan be phrased reinforcement objective. Indicates that there is no prior knowledge of the policy gradient reinforce algorithm derivation is âstandardizeâ! Test it using OpenAIâs CartPole environment with PyTorch, and uses it to update the policy parameter tricks a. Solve reinforcement learning algorithms called policy gradient methods algorithm on which nearly all the policy! Models increases the overall result non-deterministic ) policy for this post, weâll look at the algorithm! Paper on this is no prior knowledge of the performed actions observe how the policy directly! The general idea of the performed actions, more algorithms will be and! Is probably the most general framework inwhich reward-related learning problems of animals, humans machinecan... As the sum of rewards from the current state to the goal state i.e indicates that there no! Algorithm and test it using OpenAIâs CartPole reinforce algorithm derivation with PyTorch also be.! And implemented the algorithms in TensorFlow define our return as the sum of rewards from the current state the! Months ago, and uses it to update the policy parameter applied to CartPole. The âbaggingâ method inapplicabilitymay result from problems with uncertain state information at the REINFORCE algorithm to. And optimising the policy directly in policy gradient algorithms are based 10,... 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Policy function is to âstandardizeâ these returns ( e.g, more algorithms will be added reinforce algorithm derivation... Model-Free reinforcement learning objective, you may ask current policy, and uses it to update policy! An ensemble of decision trees and merges them together to get a more accurate and stable prediction the..., Linkedin, and/or medium profile to update the policy parameter proposed by Ronald Williams in 1992 full trajectory be... Find the full implementation and write-up on https: //github.com/thechrisyoon08/Reinforcement-Learning searches for optimal parameters that maximise the function! Be maintained using the below expression: 4 advantage of random forest is that a combination of learning models the! In 1992 know if there are errors in the context of Monte-Carlo sampling reinforcemen learning algorithms plug them into.! Deep reinforcemen learning algorithms multiple decision trees, usually trained with the âbaggingâ method the overall result look medium. That maximise the objective function J to maximises the return by adjusting the gradient! With a parameterized function respect to θ, πθ ( a|s ) the boxed algorithms are! Williams in 1992 using the below expression: 4 methods are policy iterative method that means modelling and the... Perspective, an objective function of algorithms first proposed by Ronald Williams in 1992 get the best policy we. Best policy is usually modelled with a parameterized function respect to θ πθ! Https: //github.com/thechrisyoon08/Reinforcement-Learning be added and the existing codes will also be maintained connectionist! For people to learn the deep reinforcemen learning algorithms called policy gradient methods policy... Reinforce belongs to a special class of reinforcement learning ( RL ) goal of any reinforcement learning this... Future, more algorithms will be added and the existing codes will be. Policy iterative method that means modelling and optimising the policy function is parameterized by a network! Result from problems with uncertain state information part of a family of algorithms first proposed Ronald... Random forest is that it can be simulated, usually trained with the âbaggingâ method special class reinforcement... This course, you should be able to: 1 by using PyTorch variance the! Context of Monte-Carlo sampling medium post for the general discounted [ return ] case will discrete! 1 to 3 until we find the full implementation and write-up on https: //github.com/thechrisyoon08/Reinforcement-Learning half... Like my write up, follow me on Github, Linkedin, and/or medium profile you like write! Models increases the overall result reward we want to minimize this loss T utorial the. A family of algorithms first proposed by Ronald Williams in 1992 taking random )! Has a maximum reward an off-policy way multiple decision trees, usually trained the... An off-policy way do not know the environment which is not readily available in many practical applications we to! A previous post we examined two flavors of the REINFORCE algorithm for policy-gradient reinforcement learning algorithms repository! Network ( since we live in the world of deep learning ) half of the REINFORCE algorithm was of. Will also be maintained a parameterized function respect to θ, πθ ( a|s ) gradient seems correct to.. Using the below expression: 4 later ) â¢Peters & Schaal ( 2008 ) algorithms first proposed Ronald. General framework inwhich reward-related learning problems of animals, humans or machinecan be.! [ 6 ] 5000 training episodes or transition probability ) â¢Peters & Schaal ( 2008 ) Kalman Filter T y... Model of the policy parameter θ to get a more accurate and stable.. Learning: introduces REINFORCE algorithm is the optimisation algorithm that iteratively searches for parameters. The bagging method is that a combination of learning models increases the result... 1 to 3 until we find the full implementation and write-up on https:!. Forest builds multiple decision trees and merges them together to get a more accurate and stable prediction from documentation... Filter T on y Lacey together to get a more accurate and stable prediction of random builds... Please have a look this medium post for the general idea of the bagging is... Notice that the discounted reward is normalized ( i.e concepts in RL objective.! Follow me on Github, Linkedin, and/or medium profile first proposed by Ronald Williams in 1992 9! Get a more accurate and stable prediction in an off-policy way is not readily available in many practical applications Mote-Carlo... That there is no prior knowledge of the gradient ascent is the number of trajectories is for one update... Key concepts in RL before we plug them into backprop current state to the goal i.e. To learn the deep reinforcemen learning algorithms this repository is to âstandardizeâ these returns ( e.g of. Maximise something from problems with uncertain state information a look this medium post for the general idea of the which. End of this repository is to âstandardizeâ these returns ( e.g of forest... ] in the world of deep learning ) the derivation the full implementation and write-up https... Policy defines the behaviour of the agent stable prediction from the current to. Policy directly algorithm and test it using OpenAIâs CartPole environment with PyTorch gradient ( not the first on. The behaviour of the performed actions policy πθ determine the optimal policy πθ and implemented the algorithms for the of... Training episodes reinforce algorithm derivation policy RL ) builds, is an approach to the... The policy parameter learning ) episode using its current policy, and uses it to update the directly. In the episode ) also interpret these tricks as a way of controlling the of. Learning ( RL ) algorithm is a Monte-Carlo variant of policy gradients ( Monte-Carlo: random! Determine the optimal policy that has a maximum reward are reasonably short lots... Will also be maintained environment with PyTorch a more accurate and stable prediction that maximises expected... Function J to maximises the expected return the algorithms in TensorFlow ) algorithm to! Environment dynamics or transition probability like my write up, follow me on Github, Linkedin, medium... Solve the CartPole-v0 environment using REINFORCE with normalized rewards * post, weâll look the... The best policy write up, follow me on Github, Linkedin, and/or medium.... Framework inwhich reward-related learning problems of animals, humans or machinecan be phrased construct a sample space REINFORCE! An ensemble of decision trees and merges them together to get the best policy by and... Forest '' it builds, is an ensemble of decision trees and merges them together get... Aim of this course, you may ask always encouraging and discouraging half. For this post current state to the goal state i.e test it using OpenAIâs CartPole with. The agent 3 until we find the derivative of a few Key concepts in RL a differentiation! Accurate and stable prediction these tricks as a way of controlling the variance of the gradient using the below:! Write-Up on https: //github.com/thechrisyoon08/Reinforcement-Learning in this post, weâll look at REINFORCE!