welcome to deep reinforcement learning part 2

\bar{f}\left(\delta \mathbf{x}_{t}, \delta \mathbf{u}_{t}\right)=\mathbf{F}_{t}\begin{bmatrix} \bar{c}\left(\delta \mathbf{x}_{t}, \delta \mathbf{u}_{t}\right)=\frac{1}{2}\begin{bmatrix} \], \[ \mathbf{x}_{T} \\ \mathbf{Q}_{T-1}=\mathbf{C}_{T-1}+\mathbf{F}_{T-1}^{T} \mathbf{V}_{T} \mathbf{F}_{T-1} \\ In this part, we will implement a simple example of Q learning using the R programming language from scratch. \text {s.t.} {\mathbf{x}_{T-1}} \\ { p \left( \mathbf { x } _ { t + 1 } | \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) = \mathcal { N } \left( f \left( \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) , \Sigma \right) } \\ As I promised in the second part I will go deeper in model-free reinforcement learning (for prediction and control), giving an overview on Monte Carlo (MC) methods. Welcome to Deep Reinforcement Learning 2.0! \begin{align*} In this course, we will learn and implement a new incredibly smart AI model, called the Twin-Delayed DDPG, which combines state of the art techniques in Artificial Intelligence including continuous Double Deep Q-Learning… (Note: This post is a follow up of the first part, in case you missed it, please take a look at it here) In the previous article, we learned how to frame our problem into a Reinforcement Learning… \mathbf{x}_{T} \\ In the past decade deep RL has achieved remarkable results on a range of problems, from single and multiplayer games–such as Go, Atari games, and DotA 2–to robotics. Deep Reinforcement Learning (Part 2) Posted on 2020-02-06 Edited on 2020-02-12 In Computer Science Views: Symbols count in article: 23k Reading time ≈ 58 mins. However, resampling with replacement is usually unnecessary, because SGD and random initialization usually makes the models sufficiently independent. \], \[ You learnt the foundation of reinforcement learning, the dynamic programming approach. Welcome to Cutting-Edge AI! p(\mathbf{x}_{t+1} | \mathbf{x}_{t}, \mathbf{u}_{t}) = \mathcal{N}\left( \mathbf { F } _ { t } \left[ \begin{array} { c } { \mathbf { x } _ { t } } \\ { \mathbf { u } _ { t } } \end{array} \right] + \mathbf { f } _ { t }, \Sigma_t \right) \mathbf{u}_{t}-\hat{\mathbf{u}}_{t} Q\left(\mathbf{x}_{T-1}, \mathbf{u}_{T-1}\right)=\text { const }+\frac{1}{2}\begin{bmatrix} \], \[ This is where the term deep reinforcement learning comes from. Welcome to Deep Reinforcement Learning 2.0! The model is so strong that for the first time in our courses, we are able to solve the most challenging virtual AI applications (training an ant/spider and a half humanoid to walk and run across a field). Deep Deterministic Policy Gradient (DDPG), The Foundation Techniques of Deep Reinforcement Learning, How to implement a state of the art AI model that is over performing the most challenging virtual applications, Don't Miss Any Course Join Our Telegram Channel, Some maths basics like knowing what is a differentiation or a gradient, A bit of programming knowledge (classes and objects), Data Scientists who want to take their AI Skills to the next level, AI experts who want to expand on the field of applications, Engineers who work in technology and automation, Businessmen and companies who want to get ahead of the game, Students in tech-related programs who want to pursue a career in Data Science, Machine Learning, or Artificial Intelligence, Anyone passionate about Artificial Intelligence. Bayesian linear regression: use favorite global model as prior. \mathbf{x}_{t}-\hat{\mathbf{x}}_{t} \\ \], \(\mathcal { D } = \left\{ \left( \mathbf { s } , \mathbf { a } , \mathbf { s } ^ { \prime } \right) _ { i } \right\}\), \(\sum _ { i } \left\| f \left( \mathbf { s } _ { i } , \mathbf { a } _ { i } \right) - \mathbf { s } _ { i } ^ { \prime } \right\| ^ { 2 }\), \(\left( \mathbf { s } , \mathbf { a } , \mathbf { s } ^ { \prime } \right)\), \(p(\mathbf{s}_{t+1} | \mathbf{s}_t, \mathbf{a}_t)\), \(\int p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}, \theta\right) p(\theta | \mathcal{D}) d \theta\), \[ \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T \] For stochastic closed-loop system, the objective is: \[ References [1] David Silver, Aja Huang, Chris J Maddison, et al. 484–489. \DeclareMathOperator*{\argmin}{\arg\min} We'll assume you're ok with this, but you can opt-out if you wish. \begin{align*} In part 1 we introduced Q-learning as a concept with a pen and paper example.. Any Sufficiently Advanced Technology is Indistinguishable from Magic. Further Reading: A gentle Introduction to Deep Learning Basic model-based RL suffers from overfitting problem and can easily stuck in local minimum since in step 3 we only take actions for which we think the expectation reward is high. }\mathbf { x } _ { t } = f \left( \mathbf { x } _ { t - 1 } , \mathbf { u } _ { t - 1 } \right) \]. \] For stochastic open-loop system, the objective is: \[ \] and run LQR with \(\bar{f}, \bar{c}, \delta \mathbf{x}_t, \delta \mathbf{u}_t\). {\mathbf{u}_{T-1}} \mathbf{v}_{T} = &\mathbf{c}_{\mathbf{x}_{T}}+\mathbf{C}_{\mathbf{x}_{T}, \mathbf{u}_{T}} \mathbf{k}_{T}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} \mathbf{k}_{T} Q\left(\mathbf{x}_{T-1}, \mathbf{u}_{T-1}\right)=\text { const } + \frac{1}{2}\begin{bmatrix} \bar{c}\left(\delta \mathbf{x}_{t}, \delta \mathbf{u}_{t}\right)=\frac{1}{2}\begin{bmatrix} \] Let \(\delta \mathbf{x}_{t} = \mathbf{x}_{t} - \hat{\mathbf{x}}_{t}\), \(\delta \mathbf{u}_{t} = \mathbf{u}_{t} - \hat{\mathbf{u}}_{t}\). This is technically Deep Learning in Python part 11 of my deep learning series, and my 3rd reinforcement learning course. \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T We’ll first start out by introducing the absolute basics to build a solid ground for us to run. \end{equation} \delta \mathbf{u}_{t} \], \[ \max _ { \phi } \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \sum _ { t = 1 } ^ { T } \mathbb{E}_{\left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } \right) \sim p \left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } \right)} \left[ \log p _ { \phi } \left( \mathbf { s } _ { t + 1 , i } | \mathbf { s } _ { t , i } , \mathbf { a } _ { t , i } \right) + \log p _ { \phi } \left( \mathbf { o } _ { t , i } | \mathbf { s } _ { t , i } \right) \right] \], \(\bar{f}, \bar{c}, \delta \mathbf{x}_t, \delta \mathbf{u}_t\), \(\mathbf{F}_{t}=\nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} f\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\), \(\mathbf{c}_{t}=\nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\), \(\mathbf{C}_{t}=\nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}}^{2} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\), \(\delta \mathbf{x}_t, \delta \mathbf{u}_t\), \(\mathbf{u}_{t} = \mathbf{K}_{t} \mathbf{x}_{t} + \alpha \mathbf{k}_{t} + \hat{\mathbf{u}}_t\), \[ In this course, we will learn and implement a new incredibly smart AI model, called the Twin-Delayed DDPG, which combines state of the art techniques in Artificial Intelligence including continuous Double Deep Q-Learning, Policy Gradient, and Actor-Critic. As promised, in this video, we’re going to write the code to implement our first reinforcement learning algorithm. \end{bmatrix}+\begin{bmatrix} \max _ { \phi , \psi } \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \sum _ { t = 1 } ^ { T } \log p _ { \phi } \left( g _ { \psi } \left( \mathbf { o } _ { t + 1 , i } \right) | g _ { \psi } \left( \mathbf { o } _ { t , i } \right) , \mathbf { a } _ { t , i } \right) + \log p _ { \phi } \left( \mathbf { o } _ { t , i } | g _ { \psi } \left( \mathbf { o } _ { t , i } \right) \right) + \log p _ { \phi } \left( r _ { t , i } | g _ { \psi } \left( \mathbf { o } _ { t , i } \right) \right) \]. \] the algorithm stays the same. Tensorforce is a deep reinforcement learning framework based on Tensorflow. \begin{equation} Welcome to Deep Reinforcement Learning 2.0! For nonlinear case, approximate \(f\) and \(c\) by first and second order approximation respectively: \[ For standard (fully observed) model, the goal is \[ It also covers using Keras to construct a deep Q-learning network that learns within a simulated video game environment. p_{\theta}\left(\mathbf{s}_{1}, \ldots, \mathbf{s}_{T} | \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}\right)=p\left(\mathbf{s}_{1}\right) \prod_{t=1}^{T} p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}\right) \\ After the paper was published on Nature in 2015, a lot of research institutes joined this field because deep neural network can empower RL to directly deal with high dimensional states like images, thanks to techniques used in DQN. \label{dol} \mathbf{x}_{t}-\hat{\mathbf{x}}_{t} \\ Deep Learning - Reinforcement Learning Part 2. \mathbf{x}_{t+1} = f(\mathbf{x}_{t}, \mathbf{u}_{t}) \min _ { \mathbf { u } _ { 1 } , \ldots , \mathbf { u } _ { T }, \mathbf { x } _ { 1 } , \ldots , \mathbf { x } _ { T } } \sum _ { t = 1 } ^ { T } c \left( \mathbf { x } _ { t } , \mathbf { u } _ { t } \right)\quad \text { s.t. \] At step \(T-1\), first compute \(V(\mathbf{x}_T)\): \[ Welcome to the second part of the dissecting reinforcement learning series. A free course from beginner to expert. \mathbf{H}=\nabla_{\mathbf{x}}^{2} g(\hat{\mathbf{x}}) \\ &{ \mathbf { k } _ { t } = - \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { u } _ { t } } ^ { - 1 } \mathbf { q } _ { \mathbf { u } _ { t } } } \\ I’m Brian, and welcome to a MATLAB Tech Talk. \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T \begin{equation} \end{bmatrix}^{T} \mathbf{c}_{T} \\ Video References: \end{bmatrix}+\frac{1}{2}\begin{bmatrix} \]. Welcome to the second part of my reinforcement learning adventure, in which I will be going over my encounter with the Markov decision process and the Bellman equation. Welcome to the most fascinating topic in Artificial Intelligence: Deep Reinforcement Learning. \delta \mathbf{u}_{t} &{ \mathbf { K } _ { t } = - \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { u } _ { t } } ^ { - 1 } \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { x } _ { t } } } \\ \int p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}, \theta\right) p(\theta | \mathcal{D}) d \theta \approx \frac{1}{N} \sum_{i} p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}, \theta_{i}\right) Title: Reinforcement Learning Part II Author: karim Created Date: 4/7/2019 6:00:35 PM \pi=\argmax _{\pi} E_{\tau \sim p(\tau)}\left[\sum_{t} r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)\right] \mathbf{x}_{T-1} \\ \delta \mathbf{x}_{t} \\ \] Take the gradient and set it to \(0\) to get \[ \delta \mathbf{u}_{t} \end{bmatrix}^{T} \nabla_{\mathbf{x}_{t}, u_{t}}^{2} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\begin{bmatrix} \end{bmatrix}^{T} \mathbf{Q}_{T-1}\begin{bmatrix} Link to Sutton’s Reinforcement Learning in its 2018 draft, including Deep Q learning and Alpha Go details. { \mathbf { A } _ { t } = \frac { d f } { d \mathbf { x } _ { t } } \quad \mathbf { B } _ { t } = \frac { d f } { d \mathbf { u } _ { t } } } Training Deep Q Learning and Deep Q Networks (DQN) Intro and Agent - Reinforcement Learning w/ Python Tutorial p.6. \mathbf{C}_{T} =\begin{bmatrix} \end{bmatrix}\\ &= \mathbf{K}_{T-1}\mathbf{x}_{T-1} + \mathbf{k}_{T-1} \mathbf{x}_{t}-\hat{\mathbf{x}}_{t} \\ \(p(\mathbf{x}_{t+1} | \mathbf{x}_t, \mathbf{u}_t)\), \(p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}\right)\), \[ If you would like to understand the RL, Q-learning, and key terms please read Part 1. \mathbf{H}=\nabla_{\mathbf{x}}^{2} g(\hat{\mathbf{x}}) \\ \mathbf{u}_{T-1} f\left(\mathbf{x}_{t}, \mathbf{u}_{t}\right)-f\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right) \approx \nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} f\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\begin{bmatrix} There are two different ways to optimize \(\eqref{dol}\): shooting method: optimize over actions only. p_{\theta}\left(\mathbf{s}_{1}, \ldots, \mathbf{s}_{T} | \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}\right)=p\left(\mathbf{s}_{1}\right) \prod_{t=1}^{T} p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}\right) \\ \int p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}, \theta\right) p(\theta | \mathcal{D}) d \theta \approx \frac{1}{N} \sum_{i} p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}, \theta_{i}\right) \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}=\argmax _{\mathbf{a}_{1}, \ldots, \mathbf{a}_{T}} E\left[\sum_{t} r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) | \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}\right] \mathbf{g}=\nabla_{\mathbf{x}} g(\hat{\mathbf{x}}) \\ \end{bmatrix}+\begin{bmatrix} Welcome to this series on reinforcement learning! \mathbf{u}_{T-1} \begin{align*} In: Nature 529.7587 (2016), pp. \begin{align*} \mathbf{c}_{\mathbf{x}_{T}} \\ \] If we use second order dynamics approximation, the method is called differential dynamic programming (DDP). The policy would take in all of these observations and output the actuated commands. \end{bmatrix}^{T} \mathbf{c}_{T-1}+V\left(\mathbf{x}_{T}\right) \mathbf{u}_{T-1} &= -\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{u}_{T-1}}^{-1}\left(\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{x}_{T-1}} \mathbf{x}_{T-1}+\mathbf{q}_{\mathbf{u}_{T-1}}\right) \\ \mathbf{u}_{T-1} This video explains the basics of reinforcement learning: The Markov Decision Process and how to compure the expected future return. \max _ { \phi } \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \sum _ { t = 1 } ^ { T } \log p _ { \phi } \left( \mathbf { s } _ { t + 1 , i } | \mathbf { s } _ { t , i } , \mathbf { a } _ { t , i } \right) \end{bmatrix} But this approach reaches its limits pretty quickly. \label{lqrqv} \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}=\argmax _{\mathbf{a}_{1}, \ldots, \mathbf{a}_{T}} E\left[\sum_{t} r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) | \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}\right] \mathbf{C}_{\mathbf{u}_{T}, \mathbf{x}_{T}} & \mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} In part 1, we looked at the theory behind Q-learning using a very simple dungeon game with two strategies: the accountant and the gambler.This second part takes these examples, turns them into Python code and trains them in the cloud, using the Valohai deep learning management platform. To solve this problem we must consider uncertainty in the model: Bayesian neural network (BNN): In BNN, nodes are connected by distributions instead of weights. Extremely sensitive to the initial action \[ \], \(\hat{\mathbf{x}}_t, \hat{\mathbf{u}}_t, \mathbf{K}_t, \mathbf{k}_t\), \(p \left( \mathbf { u } _ { t } | \mathbf { x } _ { t } \right) = \delta(\mathbf { u } _ { t } = \hat{\mathbf { u } }_t)\), \(p \left( \mathbf { u } _ { t } | \mathbf { x } _ { t } \right) = \delta(\mathbf { u } _ { t } = \mathbf{K}_t (\mathbf{x}_t - \hat{\mathbf{x}}_t) + \mathbf{k}_t + \hat{\mathbf { u } }_t)\), \(p \left( \mathbf { u } _ { t } | \mathbf { x } _ { t } \right) = \mathcal{N}( \mathbf{K}_t (\mathbf{x}_t - \hat{\mathbf{x}}_t) + \mathbf{k}_t + \hat{\mathbf { u } }_t, \Sigma_t)\), \(\Sigma_t = \mathbf{Q}_{\mathbf{u}_t, \mathbf{u}_t}^{-1}\), \(p \left( \mathbf { x } _ { t + 1 } | \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) = \mathcal { N } \left( \mathbf { A } _ { t } \mathbf { x } _ { t } + \mathbf { B } _ { t } \mathbf { u } _ { t } + \mathbf { c } , \mathbf { N } _ { t } \right)\), \(D_{\mathrm { KL }}(p(\tau) \| \bar{p}(\tau)) \le \epsilon\), \(\pi_{\mathrm{LQR}, i}(\mathbf{u}_t | \mathbf{x}_t)\), \(\tilde{c}_{k, i}(\mathbf{x}_t, \mathbf{u}_t)\), \(\pi_\theta(\mathbf{u}_t | \mathbf{x}_t)\), \(\tilde{c}_{k+1, i}(\mathbf{x}_t, \mathbf{u}_t) = c(\mathbf{x}_t, \mathbf{u}_t) - \lambda_{k+1, i} \log \pi_\theta(\mathbf{u}_t | \mathbf{x}_t)\), \[ \], \[ \] And \(\mathbf{A}_t, \mathbf{B}_t\) can be learned instead of learning \(f\). V(\mathbf{x}_T) &= \text { const } + \frac{1}{2}\begin{bmatrix} \delta \mathbf{x}_{t} \\ \], \[ \] Then we can solve it by backward recursion and forward recursion (Proof), Backward recursion: for \(t=T\) to \(1\) \[ p_i = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)} \] For multi-task transfer, train independent model for different task \(\pi_i\), then use supervised learning/distillation: \[ \end{bmatrix}^{T} \nabla_{\mathbf{x}_{t}, u_{t}}^{2} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\begin{bmatrix} Similar parameter sensitivity problems as shooting methods. \] For complex observations (high dimensionality, redundancy, partial observability), we have to separately learn. p_i = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)} \begin{align*} From the relation between \(Q\) and \(V\) we can get \[ \] Bootstrap ensembles: Train multiple models and see if they agree. \mathbf{A} = \argmax_\mathbf{A} J (\mathbf{A}) \begin{equation*} If we know the dynamics \(p(\mathbf{x}_{t+1} | \mathbf{x}_t, \mathbf{u}_t)\). Chapter 1: Introduction to Deep Reinforcement Learning V2.0. \] Plug in the model \(\mathbf{x}_{T}=f\left(\mathbf{x}_{T-1}, \mathbf{u}_{T-1}\right)\) in \(V\) and then plug in \(V\) in \(Q\) to get \[ Part 2: Doom (Deep Convolutional Q-Learning) Code Templates: Doom; Additional Reading: Richard S. Sutton and Andrew G. Barto, 1998, Reinforcement Learning: An Introduction; Volodymyr Mnih et al., 2016, Asynchronous Methods for Deep Reinforcement Learning {\mathbf{x}_{T-1}} \\ \mathbf{u}_{t} = \mathbf{K}_{t} \mathbf{x}_{t} + \mathbf{k}_{t} \\ \end{align*} \end{bmatrix}+\begin{bmatrix} This article is part of Deep Reinforcement Learning Course. \min _ { \mathbf { u } _ { 1 } , \ldots , \mathbf { u } _ { T } } c \left( \mathbf { x } _ { 1 } , \mathbf { u } _ { 1 } \right) + c \left( f \left( \mathbf { x } _ { 1 } , \mathbf { u } _ { 1 } \right) , \mathbf { u } _ { 2 } \right) + \cdots + c \left( f ( f ( \ldots ) \ldots ) , \mathbf { u } _ { T } \right) \], \[ \end{bmatrix}^{T} \mathbf{C}_{T-1} \begin{bmatrix} \quad \mathbf{s}_{t+1}=f\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) &= \frac{1}{2} \mathbf{x}_T^T \mathbf{V}_T \mathbf{x}_T + \mathbf{x}_T^T \mathbf{v}_{T} \\ \hat{\mathbf{x}} \leftarrow \arg \min _{\mathbf{x}} \frac{1}{2}(\mathbf{x}-\hat{\mathbf{x}})^{T} \mathbf{H}(\mathbf{x}-\hat{\mathbf{x}})+\mathbf{g}^{T}(\mathbf{x}-\hat{\mathbf{x}}) &\mathbf { q } _ { t } = \mathbf { c } _ { t } + \mathbf { F } _ { t } ^ { T } \mathbf { V } _ { t + 1 } \mathbf { f } _ { t } + \mathbf { F } _ { t } ^ { T } \mathbf { v } _ { t + 1 } \\ Where \(\operatorname { Score } \left( s _ { t } \right) = \frac { Q \left( s _ { t } \right) } { N \left( s _ { t } \right) } + 2 C \sqrt { \frac { 2 \ln N \left( s _ { t - 1 } \right) } { N \left( s _ { t } \right) } }\). &\mathbf { u } _ { t } \leftarrow \argmin _ { \mathbf { u } _ { t } } Q \left( \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) = \mathbf { K } _ { t } \mathbf { x } _ { t } + \mathbf { k } _ { t } \\ Welcome to Deep Reinforcement Learning 2.0! \], \[ Deep Learning - Reinforcement Learning Part 2 This video explains the basics of reinforcement learning: The Markov Decision Process and how to compure the expected future return. In part 2 we implemented the example in code and demonstrated how to execute it in the cloud.. \mathbf{u}_{t}-\hat{\mathbf{u}}_{t} \mathbf{u}_{T-1} &\mathbf { Q } _ { t } = \mathbf { C } _ { t } + \mathbf { F } _ { t } ^ { T } \mathbf { V } _ { t + 1 } \mathbf { F } _ { t } \\ Q\left(\mathbf{x}_{T-1}, \mathbf{u}_{T-1}\right)=\text { const }+\frac{1}{2}\begin{bmatrix} Train on the ensemble's predictions as soft targets \[ Similar to imitation learning, naive model can suffer from distribution mismatch problem, which can be solved by DAgger for model \(f\) instead of policy \(\pi\). In this article, I introduce Deep Q-Networ k (DQN) that is the first deep reinforcement learning method proposed by DeepMind. \mathbf{x}_{T-1} \\ \mathbf{x}_{T} \\ Hello and welcome to the first video about Deep Q-Learning and Deep Q Networks, or DQNs. Deep reinforcement learning is the combination of reinforcement learning (RL) and deep learning. Welcome to Tensorflow 2.0! We achieved decent scores after training our agent for long enough. \end{bmatrix}^{T} \mathbf{C}_{T} \begin{bmatrix} p ( \theta | \mathcal { D } ) = \prod _ { i } p \left( \theta _ { i } | \mathcal { D } \right) \\ \mathbf{c}_{T} =\begin{bmatrix} \] At step \(T\), \(V = 0\). The whole algorithm can be seen below: Choices to update controller with iLQR output \(\hat{\mathbf{x}}_t, \hat{\mathbf{u}}_t, \mathbf{K}_t, \mathbf{k}_t\): Since we assume the model is locally linear, the updated controller is only good when it is close to old controller. \mathbf{x}_{T-1} \\ \mathbf{q}_{T-1}=\mathbf{c}_{T-1}+\mathbf{F}_{T-1}^{T} \mathbf{V}_{T} \mathbf{f}_{T-1}+\mathbf{F}_{T-1}^{T} \mathbf{v}_{T} \mathbf{V}_{T} = &\mathbf{C}_{\mathbf{x}_{T}, \mathbf{x}_{T}}+\mathbf{C}_{\mathbf{x}_{T}, \mathbf{u}_{T}} \mathbf{K}_{T}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{x}_{T}}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} \mathbf{K}_{T} \\ Learn Figma for Web Design, User Interface, UI UX in an hour, 2020 Complete SEO Guide to Ranking Local Business Websites, The Web Developer Bootcamp (Updated 11/20), The Data Science Course 2020: Complete Data Science Bootcamp…, Digital Marketing Masterclass – 23 Courses in 1…, Machine Learning A-Z™: Hands-On Python & R In Data…, This website uses cookies to improve your experience. Although currently Reinforcement Learning has only a few practical applications, it is a promising area of research in AI that might become relevant in the near future. c\left(\mathbf{x}_{t}, \mathbf{u}_{t}\right)-c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right) \approx \nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\begin{bmatrix} In this third part, we will move our Q-learning approach from a Q-table to a deep neural net. \nabla_{\mathbf{u}_{T}} Q\left(\mathbf{x}_{T}, \mathbf{u}_{T}\right)=\mathbf{C}_{\mathbf{u}_{T}, \mathbf{x}_{T}} \mathbf{x}_{T}+\mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} \mathbf{u}_{T}+\mathbf{c}_{\mathbf{u}_{T}}^{T} \], \[ \end{equation} Let’s get to it! \mathbf{u}_{T-1} f\left(\mathbf{x}_{t}, \mathbf{u}_{t}\right)-f\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right) \approx \nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} f\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\begin{bmatrix} \delta \mathbf{x}_{t} \\ \mathbf{u}_{T-1} &= -\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{u}_{T-1}}^{-1}\left(\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{x}_{T-1}} \mathbf{x}_{T-1}+\mathbf{q}_{\mathbf{u}_{T-1}}\right) \\ \end{equation*} Sufficient Money is Indistinguishable from Magic. \quad \mathbf{s}_{t+1}=f\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) \end{bmatrix}^{T} \mathbf{C}_{t}\begin{bmatrix} \end{equation*} \end{bmatrix}+\begin{bmatrix} \mathbf{g}=\nabla_{\mathbf{x}} g(\hat{\mathbf{x}}) \\ \] Need to generate independent datasets to get independent models. Note: Before reading part 2, I recommend you read Beat Atari with Deep Reinforcement Learning! f \left( \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) = \mathbf { F } _ { t } \left[ \begin{array} { c } { \mathbf { x } _ { t } } \\ { \mathbf { u } _ { t } } \end{array} \right] + \mathbf { f } _ { t } \quad c \left( \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) = \frac { 1 } { 2 } \left[ \begin{array} { l } { \mathbf { x } _ { t } } \\ { \mathbf { u } _ { t } } \end{array} \right] ^ { T } \mathbf { C } _ { t } \left[ \begin{array} { l } { \mathbf { x } _ { t } } \\ { \mathbf { u } _ { t } } \end{array} \right] + \left[ \begin{array} { l } { \mathbf { x } _ { t } } \\ { \mathbf { u } _ { t } } \end{array} \right] ^ { T } \mathbf { c } _ { t } &{ \mathbf { K } _ { t } = - \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { u } _ { t } } ^ { - 1 } \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { x } _ { t } } } \\ \begin{align*} Tensorflow is Google's library for deep learning and artificial intelligence. This course introduces you to two of the most sought-after disciplines in Machine Learning: Deep Learning and Reinforcement Learning. Welcome back to this series on reinforcement learning! Q\left(\mathbf{x}_{T-1}, \mathbf{u}_{T-1}\right)=\text { const } + \frac{1}{2}\begin{bmatrix} &\mathbf { Q } _ { t } = \mathbf { C } _ { t } + \mathbf { F } _ { t } ^ { T } \mathbf { V } _ { t + 1 } \mathbf { F } _ { t } \\ \end{equation} \end{align*} \mathbf{x}_{T-1} \\ \] We have many choices to approximate \(p \left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } \right)\): Assume \(q(\mathbf{s}_t | \mathbf{o}_t)\) is deterministic, we can get single-step deterministic encoder: \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { t } ) = \delta(\mathbf{s}_t = g_\psi(\mathbf{o}_t)) \Rightarrow \mathbf { s } _ { t } = g_\psi(\mathbf { o } _ { t })\). \end{bmatrix}^{T} \mathbf{c}_{T-1}+V\left(\mathbf{x}_{T}\right) Deep RL is a type of Machine Learning where an agent learns how to behave in an environment by performing actions and seeing the results. \end{align*} \mathbf{q}_{T-1}=\mathbf{c}_{T-1}+\mathbf{F}_{T-1}^{T} \mathbf{V}_{T} \mathbf{f}_{T-1}+\mathbf{F}_{T-1}^{T} \mathbf{v}_{T} \max _ { \phi , \psi } \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \sum _ { t = 1 } ^ { T } \log p _ { \phi } \left( g _ { \psi } \left( \mathbf { o } _ { t + 1 , i } \right) | g _ { \psi } \left( \mathbf { o } _ { t , i } \right) , \mathbf { a } _ { t , i } \right) + \log p _ { \phi } \left( \mathbf { o } _ { t , i } | g _ { \psi } \left( \mathbf { o } _ { t , i } \right) \right) + \log p _ { \phi } \left( r _ { t , i } | g _ { \psi } \left( \mathbf { o } _ { t , i } \right) \right) \end{bmatrix}+\begin{bmatrix} \end{align*} \] Set the gradient \(\eqref{lqrg}\) to \(0\) and solve for \(\mathbf{u}_T\): \[ \], \[ \mathbf{u}_{t}-\hat{\mathbf{u}}_{t} Welcome to part 2 of the deep Q-learning with Deep Q Networks (DQNs) tutorials. \] Everything is differentiable here so can be trained with backprop. {\mathbf{u}_{T-1}} \label{lqrg} &= \frac{1}{2} \mathbf{x}_T^T \mathbf{V}_T \mathbf{x}_T + \mathbf{x}_T^T \mathbf{v}_{T} \\ &{ \mathbf { V } _ { t } = \mathbf { Q } _ { \mathbf { x } _ { t } , \mathbf { x } _ { t } } + \mathbf { Q } _ { \mathbf { x } _ { t } , \mathbf { u } _ { t } } \mathbf { K } _ { t } + \mathbf { K } _ { t } ^ { T } \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { x } _ { t } } + \mathbf { K } _ { t } ^ { T } \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { u } _ { t } } \mathbf { K } _ { t } } \\ In a walking robot example, the observations might be the state of every joint and the thousands of pixels from a camera sensor. This article is part of Deep Reinforcement Learning Course. \end{bmatrix}+\frac{1}{2}\begin{bmatrix} \end{bmatrix}+\begin{bmatrix} \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T &= \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T \mathbf{u}_{t}-\hat{\mathbf{u}}_{t} \], \(p \left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } \right)\), \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } )\), \(q_\psi ( \mathbf { s } _ { t }, \mathbf { s } _ { t+1} | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } )\), \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { t } )\), \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { t } ) = \delta(\mathbf{s}_t = g_\psi(\mathbf{o}_t)) \Rightarrow \mathbf { s } _ { t } = g_\psi(\mathbf { o } _ { t })\), \[ These observations and output the actuated commands to a Deep Q-learning and Deep Learning in 2018. 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