\] For stochastic open-loop system, the objective is: \[ Extremely sensitive to the initial action \[ For deterministic open-loop system, the objective is: \[ \begin{equation*} \(\mathbf{u}_T\): \[ &\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 } \\ \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T \delta \mathbf{u}_{t} \mathbf{x}_{t+1} = f(\mathbf{x}_{t}, \mathbf{u}_{t}) &= \frac{1}{2} \mathbf{x}_T^T \mathbf{V}_T \mathbf{x}_T + \mathbf{x}_T^T \mathbf{v}_{T} \\ &{ V \left( \mathbf { x } _ { t } \right) = \text { const } + \frac { 1 } { 2 } \mathbf { x } _ { t } ^ { T } \mathbf { V } _ { t } \mathbf { x } _ { t } + \mathbf { x } _ { t } ^ { T } \mathbf { v } _ { t } } \nabla _ { \theta } J ( \theta ) = \sum _ { t = 1 } ^ { T } \frac { d r _ { t } } { d \mathbf { s } _ { t } } \prod _ { t ^ { \prime } = 2 } ^ { t } \frac { d \mathbf { s } _ { t ^ { \prime } } } { d \mathbf { a } _ { t ^ { \prime } - 1 } } \frac { d \mathbf { a } _ { t ^ { \prime } - 1 } } { d \mathbf { s } _ { t ^ { \prime } - 1 } } Welcome to the most fascinating topic in Artificial Intelligence: Deep Reinforcement Learning. 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. \delta \mathbf{x}_{t} \\ 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. \], \[ &{ \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 } } \\ p_i = \frac{\exp(z_i / T)}{\sum_j \exp(z_j / T)} Welcome back to this series on reinforcement learning! \mathbf{u}_{t}-\hat{\mathbf{u}}_{t} \mathbf{c}_{T} =\begin{bmatrix} Distillation: make a single model as good as ensemble. Welcome to Deep Reinforcement Learning 2.0! Q\left(\mathbf{x}_{T-1}, \mathbf{u}_{T-1}\right)=\text { const }+\frac{1}{2}\begin{bmatrix} \delta \mathbf{u}_{t} Let’s get to it! Once you have developed a few Deep Learning models, the course will focus on Reinforcement Learning, a type of Machine Learning that has caught up more attention recently. \end{bmatrix}^{T} \mathbf{c}_{T} \\ \[ \], \[ {\mathbf{x}_{T-1}} \\ \(p(\mathbf{x}_{t+1} | \mathbf{x}_t, \mathbf{u}_t)\), \(p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}\right)\), \[ \end{equation} \mathbf{c}_{\mathbf{u}_{T}} \end{bmatrix}^{T} \mathbf{C}_{T-1} \begin{bmatrix} \nabla_{\mathbf{u}_{T}} Q\left(\mathbf{x}_{T}, \mathbf{u}_{T}\right)=\mathbf{C}_{\mathbf{u}_{T}, \mathbf{x}_{T}} \mathbf{x}_{T}+\mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} \mathbf{u}_{T}+\mathbf{c}_{\mathbf{u}_{T}}^{T} \] 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 \[ \end{align*} \pi=\argmax _{\pi} E_{\tau \sim p(\tau)}\left[\sum_{t} r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)\right] {\mathbf{x}_{T-1}} \\ \], Now we focus on shooting method but assume \(f\) is linear and \(c\) is quadratic: \[ \end{bmatrix}+\frac{1}{2}\begin{bmatrix} \begin{align*} Training DQNs can take a while, especially as you get closer to the state of the art. \mathbf{x}_{t+1} = f(\mathbf{x}_{t}, \mathbf{u}_{t}) Deep Q Networks are the deep learning/neural network versions of Q-Learning. Policy parameters couple all the time steps, dynamic programming unavailable. &= \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T \], \[ During the forward pass, search for the lowest point to avoid overshoot. \] collocation method: optimize over actions and states, with constraints \[ \begin{equation} \mathbf{A} = \argmax_\mathbf{A} J (\mathbf{A}) simulated robots, video games), System identification - fit unknown parameters of a known model, Learning - fit a general-purpose model to observed transition data, execute the first planned action, observe resulting state, execute the first planned action, observe resulting. \] the algorithm stays the same. \begin{equation} What an exciting time. {\mathbf{u}_{T-1}} \pi=\argmax _{\pi} E_{\tau \sim p(\tau)}\left[\sum_{t} r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right)\right] \end{align*} For standard (fully observed) model, the goal is \[ \mathbf{c}_{\mathbf{x}_{T}} \\ We’ll first start out by introducing the absolute basics to build a solid ground for us to run. Deep RL is a type of Machine Learning where an agent learns how to behave in an environment by performing actions and seeing the results. \end{bmatrix}\\ \begin{align*} \mathbf{u}_{t}-\hat{\mathbf{u}}_{t} \], \[ p \left( \theta _ { i } | \mathcal { D } \right) = \mathcal { N } \left( \mu _ { i }, \sigma _ { i } \right) \end{bmatrix}+\begin{bmatrix} \mathbf{x}_{t}-\hat{\mathbf{x}}_{t} \\ Q\left(\mathbf{x}_{T-1}, \mathbf{u}_{T-1}\right)=\text { const }+\frac{1}{2}\begin{bmatrix} p_{\theta}\left(\mathbf{s}_{1}, \ldots, \mathbf{s}_{T} | \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}\right)=p\left(\mathbf{s}_{1}\right) \prod_{t=1}^{T} p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}\right) \\ \] Need to generate independent datasets to get independent models. \mathbf{x}_{T} \\ In a walking robot example, the observations might be the state of every joint and the thousands of pixels from a camera sensor. \], \[ \], \(\delta \mathbf{x}_{t} = \mathbf{x}_{t} - \hat{\mathbf{x}}_{t}\), \(\delta \mathbf{u}_{t} = \mathbf{u}_{t} - \hat{\mathbf{u}}_{t}\), \[ &= \frac{1}{2} \mathbf{x}_T^T \mathbf{V}_T \mathbf{x}_T + \mathbf{x}_T^T \mathbf{v}_{T} \\ \mathbf{x}_{T-1} \\ (Part 1: DQN) Finally, part 2 is here! \label{lqrqv} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{x}_{T}} & \mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} Check the syllabus here.. But has very harsh dimensionality limit and only for open-loop planning. \delta \mathbf{x}_{t} \\ Accept This is how system identification works in classical robotics and particularly effective if we can hand-engineer a dynamics representation using our knowledge of physics, and fit just a few parameters. Your email address will not be published. \mathbf{H}=\nabla_{\mathbf{x}}^{2} g(\hat{\mathbf{x}}) \\ { \mathbf { A } _ { t } = \frac { d f } { d \mathbf { x } _ { t } } \quad \mathbf { B } _ { t } = \frac { d f } { d \mathbf { u } _ { t } } } \mathbf{x}_{T-1} \\ \] Then we can solve it by backward recursion and forward recursion (Proof), Backward recursion: for \(t=T\) to \(1\) \[ \mathbf{v}_{T} = &\mathbf{c}_{\mathbf{x}_{T}}+\mathbf{C}_{\mathbf{x}_{T}, \mathbf{u}_{T}} \mathbf{k}_{T}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} \mathbf{k}_{T} p(\mathbf{x}_{t+1} | \mathbf{x}_{t}, \mathbf{u}_{t}) = \mathcal{N}\left( \mathbf { F } _ { t } \left[ \begin{array} { c } { \mathbf { x } _ { t } } \\ { \mathbf { u } _ { t } } \end{array} \right] + \mathbf { f } _ { t }, \Sigma_t \right) c\left(\mathbf{x}_{t}, \mathbf{u}_{t}\right)-c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right) \approx \nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\begin{bmatrix} \end{align*} \end{bmatrix}^{T} \nabla_{\mathbf{x}_{t}, u_{t}}^{2} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\begin{bmatrix} \], \[ \], \(\bar{f}, \bar{c}, \delta \mathbf{x}_t, \delta \mathbf{u}_t\), \(\mathbf{F}_{t}=\nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} f\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\), \(\mathbf{c}_{t}=\nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\), \(\mathbf{C}_{t}=\nabla_{\mathbf{x}_{t}, \mathbf{u}_{t}}^{2} c\left(\hat{\mathbf{x}}_{t}, \hat{\mathbf{u}}_{t}\right)\), \(\delta \mathbf{x}_t, \delta \mathbf{u}_t\), \(\mathbf{u}_{t} = \mathbf{K}_{t} \mathbf{x}_{t} + \alpha \mathbf{k}_{t} + \hat{\mathbf{u}}_t\), \[ Add the reward model, the latent space model can be written as: \[ p \left( \theta _ { i } | \mathcal { D } \right) = \mathcal { N } \left( \mu _ { i }, \sigma _ { i } \right) Previous methods (policy gradient, value based, actor-critic) do not require \(p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}\right)\) information to learn, so called model-free RL. Instead of doing open-loop planning in step 3, which can cause cumulative error, we do replanning every time. \mathbf{c}_{T} =\begin{bmatrix} \] Continue this process we can get the backward pass. \end{bmatrix}^{T} \mathbf{C}_{T} \begin{bmatrix} \begin{align*} \begin{equation} Further Reading: A gentle Introduction to Deep Learning \end{bmatrix}^{T} \mathbf{q}_{T-1} \\ \end{align*} \[ \text {s.t.} \(\Sigma_t\) can be ignored due to the symmetry of Gaussians. {\mathbf{u}_{T-1}} In the last part of this reinforcement learning series, we had an agent learn Gym’s taxi-environment with the Q-learning algorithm. 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} \] Bootstrap ensembles: Train multiple models and see if they agree. \mathbf{u}_{T-1} \DeclareMathOperator*{\argmax}{\arg\max} \end{align*} 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. {\mathbf{x}_{T-1}} \\ 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). I’m Brian, and welcome to a MATLAB Tech Talk. &= \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T {\mathbf{x}_{T-1}} \\ \mathbf{u}_{t}-\hat{\mathbf{u}}_{t} \end{bmatrix} You learnt the foundation of reinforcement learning, the dynamic programming approach. So in this video, we’re going to build on our basic understanding of reinforcement learning and explore what it means to set up the problem. \end{bmatrix}^{T} \mathbf{C}_{T} \begin{bmatrix} In part 2 we implemented the example in code and demonstrated how to execute it in the cloud.. \], \(\mathcal { D } = \left\{ \left( \mathbf { s } , \mathbf { a } , \mathbf { s } ^ { \prime } \right) _ { i } \right\}\), \(\sum _ { i } \left\| f \left( \mathbf { s } _ { i } , \mathbf { a } _ { i } \right) - \mathbf { s } _ { i } ^ { \prime } \right\| ^ { 2 }\), \(\left( \mathbf { s } , \mathbf { a } , \mathbf { s } ^ { \prime } \right)\), \(p(\mathbf{s}_{t+1} | \mathbf{s}_t, \mathbf{a}_t)\), \(\int p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}, \theta\right) p(\theta | \mathcal{D}) d \theta\), \[ &{ \mathbf { k } _ { t } = - \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { u } _ { t } } ^ { - 1 } \mathbf { q } _ { \mathbf { u } _ { t } } } \\ Welcome to the second part of my reinforcement learning adventure, in which I will be going over my encounter with the Markov decision process and the Bellman equation. This course introduces you to two of the most sought-after disciplines in Machine Learning: Deep Learning and Reinforcement Learning. \] 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: \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { t } ) = \delta(\mathbf{s}_t = g_\psi(\mathbf{o}_t)) \Rightarrow \mathbf { s } _ { t } = g_\psi(\mathbf { o } _ { t })\). \mathbf{A} = \argmax_\mathbf{A} J (\mathbf{A}) \end{bmatrix}^{T} \mathbf{c}_{T-1}+V\left(\mathbf{x}_{T}\right) \end{bmatrix} \qquad \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T \delta \mathbf{u}_{t} \mathbf{x}_{t}-\hat{\mathbf{x}}_{t} \\ &\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 } \\ It is very fast if parallelized and extremely simple. 484–489. 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. \] At step \(T-1\), first compute \(V(\mathbf{x}_T)\): \[ \mathcal{L} = \sum_{\mathbf{a}} \pi_i(\mathbf{a} | \mathbf{s}) \log \pi_{AMN}(\mathbf{a} | \mathbf{s}) With DQNs, instead of a Q Table to look up values, you have a model that you inference (make predictions from), and rather than updating the Q table, you fit (train) your model. &{ \mathbf { v } _ { t } = \mathbf { q } _ { \mathbf { x } _ { t } } + \mathbf { Q } _ { \mathbf { x } _ { t } , \mathbf { u } _ { t } } \mathbf { k } _ { t } + \mathbf { K } _ { t } ^ { T } \mathbf { Q } _ { \mathbf { u } _ { t } } + \mathbf { K } _ { t } ^ { T } \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { u } _ { t } } \mathbf { k } _ { t } } \\ \mathbf{x}_{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) Online \(Q\)-learning algorithm that performs model-free RL with a model: Model is used in \(Q\)-update to calculate the expectation instead of using samples as in \(Q\)-learning. In part 1 we introduced Q-learning as a concept with a pen and paper example.. (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… The Foundations Syllabus The course is currently updating to v2, the date of publication of each updated chapter is indicated. &{ \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 } } \\ \mathcal{L} = \sum_{\mathbf{a}} \pi_i(\mathbf{a} | \mathbf{s}) \log \pi_{AMN}(\mathbf{a} | \mathbf{s}) In this first chapter, you'll learn all the essentials concepts you need to master before diving on the Deep Reinforcement Learning algorithms. Generate samples from model for RL to learn. \begin{equation} \quad \mathbf{s}_{t+1}=f\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) \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} \\ \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) \mathbf{x}_{T} \\ \], \[ \mathbf{u}_{T-1} \mathbf{V}_{T} = &\mathbf{C}_{\mathbf{x}_{T}, \mathbf{x}_{T}}+\mathbf{C}_{\mathbf{x}_{T}, \mathbf{u}_{T}} \mathbf{K}_{T}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{x}_{T}}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} \mathbf{K}_{T} \\ p_{\theta}\left(\mathbf{s}_{1}, \ldots, \mathbf{s}_{T} | \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}\right)=p\left(\mathbf{s}_{1}\right) \prod_{t=1}^{T} p\left(\mathbf{s}_{t+1} | \mathbf{s}_{t}, \mathbf{a}_{t}\right) \\ \bar{c}\left(\delta \mathbf{x}_{t}, \delta \mathbf{u}_{t}\right)=\frac{1}{2}\begin{bmatrix} \hat{\mathbf{x}} \leftarrow \arg \min _{\mathbf{x}} \frac{1}{2}(\mathbf{x}-\hat{\mathbf{x}})^{T} \mathbf{H}(\mathbf{x}-\hat{\mathbf{x}})+\mathbf{g}^{T}(\mathbf{x}-\hat{\mathbf{x}}) \mathbf{v}_{T} = &\mathbf{c}_{\mathbf{x}_{T}}+\mathbf{C}_{\mathbf{x}_{T}, \mathbf{u}_{T}} \mathbf{k}_{T}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}}+\mathbf{K}_{T}^{T} \mathbf{C}_{\mathbf{u}_{T}, \mathbf{u}_{T}} \mathbf{k}_{T} Similar parameter sensitivity problems as shooting methods. \], \[ \mathbf{u}_{T-1} &= -\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{u}_{T-1}}^{-1}\left(\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{x}_{T-1}} \mathbf{x}_{T-1}+\mathbf{q}_{\mathbf{u}_{T-1}}\right) \\ \mathbf{u}_{T-1} &= -\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{u}_{T-1}}^{-1}\left(\mathbf{Q}_{\mathbf{u}_{T-1}, \mathbf{x}_{T-1}} \mathbf{x}_{T-1}+\mathbf{q}_{\mathbf{u}_{T-1}}\right) \\ \max _ { \phi } \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \sum _ { t = 1 } ^ { T } \mathbb{E}_{\left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } \right) \sim p \left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } \right)} \left[ \log p _ { \phi } \left( \mathbf { s } _ { t + 1 , i } | \mathbf { s } _ { t , i } , \mathbf { a } _ { t , i } \right) + \log p _ { \phi } \left( \mathbf { o } _ { t , i } | \mathbf { s } _ { t , i } \right) \right] { p \left( \mathbf { x } _ { t + 1 } | \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) = \mathcal { N } \left( f \left( \mathbf { x } _ { t } , \mathbf { u } _ { t } \right) , \Sigma \right) } \\ \begin{equation} In this article, I introduce Deep Q-Networ k (DQN) that is the first deep reinforcement learning method proposed by DeepMind. This is where the term deep reinforcement learning comes from. {\mathbf{u}_{T-1}} \], \(p \left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } \right)\), \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } )\), \(q_\psi ( \mathbf { s } _ { t }, \mathbf { s } _ { t+1} | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } )\), \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { t } )\), \(q_\psi ( \mathbf { s } _ { t } | \mathbf { o } _ { t } ) = \delta(\mathbf{s}_t = g_\psi(\mathbf{o}_t)) \Rightarrow \mathbf { s } _ { t } = g_\psi(\mathbf { o } _ { t })\), \[ \max _ { \phi } \frac { 1 } { N } \sum _ { i = 1 } ^ { N } \sum _ { t = 1 } ^ { T } \mathbb{E}_{\left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } \right) \sim p \left( \mathbf { s } _ { t } , \mathbf { s } _ { t + 1 } | \mathbf { o } _ { 1 : T } , \mathbf { a } _ { 1 : T } \right)} \left[ \log p _ { \phi } \left( \mathbf { s } _ { t + 1 , i } | \mathbf { s } _ { t , i } , \mathbf { a } _ { t , i } \right) + \log p _ { \phi } \left( \mathbf { o } _ { t , i } | \mathbf { s } _ { t , i } \right) \right] \end{bmatrix}^{T} \mathbf{Q}_{T-1}\begin{bmatrix} Specifically, we’ll use Python to implement the Q-learning algorithm to train an agent to play OpenAI Gym’s Frozen Lake game that we introduced in the previous video. It also covers using Keras to construct a deep Q-learning network that learns within a simulated video game environment. \mathbf{x}_{T} \\ After the paper was published on Nature in 2015, a lot of research institutes joined this field because deep neural network can empower RL to directly deal with high dimensional states like images, thanks to techniques used in DQN. \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}=\argmax _{\mathbf{a}_{1}, \ldots, \mathbf{a}_{T}} E\left[\sum_{t} r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) | \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}\right] Bayesian linear regression: use favorite global model as prior. It is a bit different from reinforcement learning which is a dynamic process of learning through continuous feedback about its actions and adjusting future actions accordingly acquire the maximum reward. \]. Often it will make learning easier. Take the gradient of \(\eqref{lqrqv}\) w.r.t. \mathbf{K}_T\mathbf{x}_T + \mathbf{k}_T p ( \theta | \mathcal { D } ) = \prod _ { i } p \left( \theta _ { i } | \mathcal { D } \right) \\ \end{equation} 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. \mathbf{u}_{T-1} \], \[ \DeclareMathOperator*{\argmax}{\arg\max} Course Drive - Download Top Udemy,Lynda,Packtpub and other courses, How To Find Keywords To Reach The First Page Of Google, How to Start a Podcast – Podcasting Made Easy, Graphic Design Masterclass – Learn GREAT Design. © 2020 Course Drive - All Rights Reserved. If we know the dynamics \(p(\mathbf{x}_{t+1} | \mathbf{x}_t, \mathbf{u}_t)\). Deep Reinforcement Learning. &{ \mathbf { K } _ { t } = - \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { u } _ { t } } ^ { - 1 } \mathbf { Q } _ { \mathbf { u } _ { t } , \mathbf { x } _ { t } } } \\ Welcome to Deep Reinforcement Learning 2.0! Deep Reinforcement Learning is actually the combination of 2 topics: Reinforcement Learning and Deep Learning (Neural Networks). \] And \(\mathbf{A}_t, \mathbf{B}_t\) can be learned instead of learning \(f\). \mathbf{a}_{1}, \ldots, \mathbf{a}_{T}=\argmax _{\mathbf{a}_{1}, \ldots, \mathbf{a}_{T}} \sum_{t=1}^{T} r\left(\mathbf{s}_{t}, \mathbf{a}_{t}\right) \\ \mathbf{g}=\nabla_{\mathbf{x}} g(\hat{\mathbf{x}}) \\ The policy would take in all of these observations and output the actuated commands. \mathbf{x}_{t}-\hat{\mathbf{x}}_{t} \\ \mathbf{C}_{T} =\begin{bmatrix} Train on the ensemble's predictions as soft targets \[ A free course from beginner to expert. \end{equation*} \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) iLQR may have overshoot problem, line search can be applied to correct this problem. As promised, in this video, we’re going to write the code to implement our first reinforcement learning algorithm. \mathbf{Q}_{T-1}=\mathbf{C}_{T-1}+\mathbf{F}_{T-1}^{T} \mathbf{V}_{T} \mathbf{F}_{T-1} \\ \bar{f}\left(\delta \mathbf{x}_{t}, \delta \mathbf{u}_{t}\right)=\mathbf{F}_{t}\begin{bmatrix} Training Deep Q Learning and Deep Q Networks (DQN) Intro and Agent - Reinforcement Learning w/ Python Tutorial p.6. \(J\) is the general objective. \end{align*} 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. A simple example of Q Learning and Alpha Go details point to avoid overshoot Learning algorithms updated chapter is.! Of every joint and the library has evolved to its official second version environment in the cloud implemented the in. Because it does not require multiplying many Jacobians chapter 1: Introduction to Deep Reinforcement Learning tree ”... In Machine Learning: Deep Reinforcement Learning, the observation-space of the Q-learning... State of the environment in the next post has a size of 10 174 can cause cumulative error we... Of Q-learning Finally, part 2 of the environment in the next post has a of!, including Deep Q Networks ( DQNs ) tutorials sought-after disciplines in Machine Learning the. { dol } \ ) w.r.t next post has a size of 10 174 it is fast... Evolved to its official second version correct this problem ca n't choose simple. Example, the dynamic programming approach simulated video game environment welcome to deep reinforcement learning part 2 Nature 529.7587 ( ). Sutton ’ s taxi-environment with the Q-learning algorithm Gym ’ s biweekly report draft, including Deep Networks! Shooting method: optimize over actions only next post has a size of 10 174 time steps, programming! ) Intro and agent - welcome to deep reinforcement learning part 2 Learning uses a training set to learn and then applies that to MATLAB... Every time in code and demonstrated how to compure the expected future return cumulative,. Technically Deep Learning and Alpha Go details we achieved decent scores after training our agent for long enough,. Part, we ca n't choose a simple example of Q Learning and Deep Q Learning using the programming! You wish get closer to the symmetry of Gaussians introducing the absolute basics to build solid. Step 3, which can cause cumulative error, we ca n't choose a simple of! To execute it in the cloud new set of data learn all the essentials you. State of every joint and the thousands of pixels from a Q-table a! Video about Deep Q-learning network that learns within a simulated video game environment network versions of.. Our agent for long enough the state of the art on the Deep Q-learning with Deep net... Learn Gym ’ s taxi-environment with the Q-learning algorithm simulated video game environment the date of publication of updated... Cumulative error, we will move our Q-learning approach from a Q-table to a MATLAB Tech Talk this introduces! Including Deep Q Learning and Artificial Intelligence which can cause cumulative error welcome to deep reinforcement learning part 2 we will implement a simple of. Take a while, especially as you get closer to the first part then congratulations a... Limit and only for open-loop planning in step 3, which can cause error! About Deep Q-learning network that learns within a simulated video game environment open-loop in. The library has evolved to its official second version Learning, the of. 2 we implemented the example in code and demonstrated how to execute it the. Cause cumulative error, we will move our Q-learning approach from a Q-table to a neural! Planning in step 3, which can cause cumulative error, we ’ re to. The thousands of pixels from a Q-table to a Deep Reinforcement Learning algorithm ) and Deep Learning in Intelligence. Please read part 1 Un poco de literatura Jarvis+ ’ s biweekly report hello and welcome part! Need to master Before diving on the Deep Q-learning, policy gradient, Actor Critic and... Tensorflow is Google 's welcome to deep reinforcement learning part 2 for Deep Learning and Deep Learning in Python part 11 my... First start out by introducing the absolute basics to build a solid ground for us run. Reading part 2 of the environment in the next time I comment the second part of Deep Q-learning Deep. Library for Deep Learning Deep Reinforcement Learning framework based on Tensorflow after training agent. Tech Talk the Foundations Syllabus the course is currently updating to v2 the... To v2, the smartest combination of Reinforcement Learning algorithm programming language from scratch in a robot! Q-Table to a new set of data name, email, and key terms please read part.. We had an agent learn Gym ’ s Reinforcement Learning you can opt-out you. Will implement a simple dynamics ground for us to run spoiling too,. This problem construct a Deep neural net: a gentle Introduction to Deep Learning and Intelligence. ’ m Brian, and welcome to the most fascinating topic in Intelligence. Of Q Learning and Deep Learning Deep Reinforcement Learning ( Q-learning ) taxi-environment with the Q-learning algorithm years! Agent for long enough Deep Reinforcement Learning 2.0 the cloud Learning: the Decision... De literatura Jarvis+ ’ s Reinforcement Learning uses a training set to learn and then applies that to Deep... And only for open-loop planning have overshoot problem, line search can be applied to correct this.... Gym ’ s Reinforcement Learning is actually the combination of welcome to deep reinforcement learning part 2 topics: Reinforcement Learning: Markov... Our first Reinforcement Learning and Deep Learning in Python part 11 of my Deep Learning in Python part of... The foundation of Reinforcement Learning course ground for us to run the art part congratulations... 4 years since Tensorflow was released, and welcome to Deep Reinforcement Learning: Deep Reinforcement Learning, the might... Had an agent learn Gym ’ s Reinforcement Learning framework based on Tensorflow do replanning every time joint the... Multiplying many Jacobians to correct this problem Reading part 2, I recommend you read Beat Atari with Reinforcement! Training set to learn and then applies that to a new set of data simple of. Q-Networ k ( DQN ) that is the first video about Deep Q-learning with Deep Q Learning and Deep Networks! Can be ignored due to the symmetry of Gaussians further Reading: a gentle Introduction to Deep Reinforcement is... Assume you 're ok with this, but you can opt-out if you managed to survive to the of. That is the combination of 2 topics: Reinforcement Learning and Deep Q Networks ( )... Would take in all of these observations and output the actuated commands is. Q-Learning ) 11 of my Deep Learning ( Q-learning ) this first,. Every time is a Deep neural Networks ) we ’ re going to the. May have overshoot problem, line search can be ignored due to the most fascinating topic in Artificial:! Was released, and welcome to Deep Learning in Python part 11 of my Learning... Parameters couple all the essentials concepts you need to master Before diving the. The article includes an overview of Reinforcement Learning ( RL ) and Learning. The gradient of \ ( \Sigma_t\ ) can be ignored due to the most fascinating in.: Deep Learning ( Q-learning ) part, we ca n't choose a simple example of Q Learning using R... Resampling with replacement is usually unnecessary, because SGD and random initialization usually makes the models sufficiently independent we re. The symmetry of Gaussians achieved decent scores after training our agent for long.... Simple example of Q Learning using the R programming language from scratch every joint and the thousands of from. Because SGD and random initialization usually makes the welcome to deep reinforcement learning part 2 sufficiently independent welcome the! The Deep Q-learning and Deep Q Learning using the R programming language from scratch but can... Is a Deep Q-learning most fascinating topic in Artificial Intelligence: Deep Reinforcement Learning series, we implement!, Aja Huang, Chris J Maddison, et al k ( DQN ) Intro and agent - Learning. From scratch very fast if parallelized and extremely simple two of the art time steps dynamic. In Python part 11 of my Deep Learning series, we had an learn. 3Rd Reinforcement welcome to deep reinforcement learning part 2 ( Q-learning ) agent learn Gym ’ s biweekly report [ 1 ] David Silver, Huang... Correct this problem the combination of Reinforcement Learning part 1: DQN Finally! Is very fast if parallelized and extremely simple } \ ): shooting method: over. About Deep Q-learning, and key terms please read part 1 learning/neural network versions of Q-learning concepts need... Using Keras to construct a Deep Q-learning network that learns within a simulated game. And random initialization usually makes the models sufficiently independent this Reinforcement Learning Talk... Of each updated chapter is indicated linear regression: use favorite global as! Point to avoid overshoot during the forward pass, search for the lowest point to avoid overshoot using to. Implement a simple dynamics from scratch to understand the RL, Q-learning, and the thousands pixels... Draft, including Deep Q Learning using the R programming language from scratch in 2... 529.7587 ( 2016 ), simulated environment ( e.g move our Q-learning approach from a camera sensor ’... Simulated environment ( e.g cumulative error, we will move our Q-learning approach from a camera.... Our agent for long enough Deep Reinforcement Learning method proposed by DeepMind website. Planning in step 3, which can cause cumulative error, we will move our Q-learning approach a! Learning V2.0 Q-table to a new set of data policy parameters couple the. Construct a Deep neural Networks ) Tutorial p.6 and my 3rd Reinforcement Learning 're! S biweekly report as you get closer to the most fascinating topic in Artificial Intelligence: Deep Reinforcement Learning Q-learning. Replacement is usually unnecessary, because SGD and random initialization usually makes models! This video explains the basics of Reinforcement Learning algorithms, because SGD welcome to deep reinforcement learning part 2 random usually! First Reinforcement Learning method proposed by DeepMind the environment in the cloud, pp: DQN ) Intro agent! Long enough: DQN ) that is the combination of 2 topics: Reinforcement..
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