# Deep Reinforcement Learning – Winter 2019/20

In recent years, reinforcement learning has been combined with deep neural networks, giving rise to game agents with super-human performance (for example for Go, chess, or 1v1 Dota2, capable of being trained solely by self-play), datacenter cooling algorithms being 50% more efficient than trained human operators, or improved machine translation. The goal of the course is to introduce reinforcement learning employing deep neural networks, focusing both on the theory and on practical implementations.

Python programming skills and TensorFlow skills (or any other deep learning framework) are required, to the extent of the NPFL114 course. No previous knowledge of reinforcement learning is necessary.

SIS code: NPFL122
Semester: winter
E-credits: 6
Examination: 2/2 C+Ex
Guarantor: Milan Straka

### Timespace Coordinates

• lecture: the lecture is held on Monday 15:40 in S4; first lecture is on Oct 07
• practicals: there are two parallel practicals, on Monday 17:20 in SU1 and on Tuesday 10:40 in SU2; first practicals are on Oct {07,08}

### Lectures

The lecture content, including references to study materials.

The main study material is the Reinforcement Learning: An Introduction; second edition by Richard S. Sutton and Andrew G. Barto (reffered to as RLB). It is available online and also as a hardcopy.

References to study materials cover all theory required at the exam, and sometimes even more – the references in italics cover topics not required for the exam.

### 1. Introduction to Reinforcement Learning

Oct 07 Slides PDF Slides Video

multiarmed_bandits

• History of RL [Chapter 1 of RLB]
• Multi-armed bandits [Chapter 2 of RLB]

### 2. Markov Decision Process, Optimal Solutions, Monte Carlo Methods

• Markov Decision Process [Sections 3-3.3 of RLB]
• Policies and Value Functions [Sections 3.5-3.6 of RLB]
• Value Iteration [Sections 4 and 4.4 of RLB]
• Proof of convergence only in slides
• Policy Iteration [Sections 4.1-4.3 of RLB]
• Generalized Policy Iteration [Section 4.6 or RLB]
• Monte Carlo Methods [Sections 5-5.4 of RLB]

### 3. Temporal Difference Methods, Off-Policy Methods

• Model-free and model-based methods, using state-value or action-value functions [Chapter 8 before Section 8.1, and Section 6.8 of RLB]
• Temporal-difference methods [Sections 6-6.3 of RLB]
• Sarsa [Section 6.4 of RLB]
• Q-learning [Section 6.5 of RLB]
• Off-policy Monte Carlo Methods [Sections 5.5-5.7 of RLB]
• Expected Sarsa [Section 6.6 of RLB]

### 4. Self-Study: N-step Temporal Difference Methods

Nov 04 Slides PDF Slides

This is a self-study lecture.

• N-step TD policy evaluation [Section 7.1 of RLB]
• N-step Sarsa [Section 7.2 of RLB]
• Off-policy n-step Sarsa [Section 7.3 of RLB]
• Tree backup algorithm [Section 7.5 of RLB]

### 5. Function Approximation, Deep Q Network

• Function approximation [Sections 9-9.3 of RLB]
• Tile coding [Section 9.5.4 of RLB]
• Linear function approximation [Section 9.4 of RLB, without the Proof of Convergence if Linear TD(0)]
• Semi-Gradient TD methods [Sections 9.3, 10-10.2 of RLB]
• Off-policy function approximation TD divergence [Sections 11.2-11.3 of RLB]
• Deep Q Network [Volodymyr Mnih et al.: Human-level control through deep reinforcement learning]

### 7. Gradient Based Methods

• Policy Gradient Methods [Sections 13-13.1 of RLB]
• Policy Gradient Theorem [Section 13.2 of RLB]
• REINFORCE algorithm [Section 13.3 of RLB]
• REINFORCE with baseline algorithm [Section 13.4 of RLB]
• Actor-Critic methods [Section 13.5 of RLB, without the eligibility traces variant]
• A3C and asynchronous RL [Volodymyr Mnih et al.: Asynchronous Methods for Deep Reinforcement Learning]

### 10. V-trace, PopArt Normalization, Partially Observable MDPs

Dec 16 Slides PDF Slides Video

### Requirements

To pass the practicals, you need to obtain at least 80 points, excluding the bonus points. Note that up to 40 points above 80 will be transfered to the exam.

### Environment

The tasks are evaluated automatically using the ReCodEx Code Examiner. The evaluation is performed using Python 3.6, TensorFlow 2.0.0, NumPy 1.17.2 and OpenAI Gym 0.14.0. For those using PyTorch, CPU version 1.2.0 is available.

You can install TensorFlow and Gym either to user packages using pip3 install --user tensorflow==2.0.0 gym==0.14.0 scipy box2d-py atari-py (with the last three backages being optinal dependencies of gym), or create a virtual environment using python3 -m venv VENV_DIR and then installing the packages inside it by running VENV_DIR/bin/pip3 install .... On Windows, you can use third-party precompiled versions of box2d-py.

### Teamwork

Working in teams of size 2 (or at most 3) is encouraged. All members of the team must submit in ReCodEx individually, but can have exactly the same sources/models/results. However, each such solution must explicitly list all members of the team to allow plagiarism detection using this template.

### Submitting Data Files to ReCodEx

Because ReCodEx allows submitting only Python sources in our settings, we need to embed models and other non-Python data into Python sources. You can use the embed.py script, which compresses the given files and directories and embeds them into a Python module, which extracts them when imported or executed.

### multiarmed_bandits

Deadline: Oct 20, 23:59  8 points

Perform a parameter study of various approaches to solving multiarmed bandits. For every hyperparameter choice, perform 100 episodes, each consisting of 1000 trials, and report the average and standard deviation of the 100 episode returns.

Start with the multiarmed_bandits.py template, which defines MultiArmedBandits environment. We use API based on OpenAI Gym Environment class, notably the following two methods:

• reset() → new_state: starts a new episode
• step(action) → new_state, reward, done, info: perform the chosen action in the environment, returning the new state, obtained reward, a boolean flag indicating an end of episode, and additional environment-specific information Of course, the states are not used by the multiarmed bandits (None is returned).

Your goal is to implement the following modes of calculation. In addition to submitting the solution to ReCodEx, you should use multiarmed_bandits_draw.py to plots the results in a graph.

• greedy [2 points]: perform $ε$-greedy search with parameter epsilon, computing the value function using averaging. (Results for $ε ∈ \{1/64, 1/32, 1/16, 1/8, 1/4\}$ are plotted.)
• greedy and alpha$≠0$ [1 point]: perform $ε$-greedy search with parameter epsilon and initial function estimate of 0, using fixed learning rate alpha. (Results for $α=0.15$ and $ε ∈ \{1/64, 1/32, 1/16, 1/8, 1/4\}$ are plotted.)
• greedy, alpha$≠0$ and initial$≠0$ [1 point]: perform $ε$-greedy search with parameter epsilon, given initial value as starting value function and fixed learning rate alpha. (Results for initial$=1$, $α=0.15$ and $ε ∈ \{1/128, 1/64, 1/32, 1/16\}$ are plotted.)
• ucb [2 points]: perform UCB search with confidence level c and computing the value function using averaging. (Results for $c ∈ \{1/4, 1/2, 1, 2, 4\}$ are plotted.)
• gradient [2 points]: choose actions according to softmax distribution, updating the parameters using SGD to maximize expected reward. (Results for $α ∈ \{1/16, 1/8, 1/4, 1/2\}$ are plotted.)

### policy_iteration

Deadline: Nov 03, 23:59  5 points

Consider the following gridworld:

Start with policy_iteration.py, which implements the gridworld mechanics, by providing the following methods:

• GridWorld.states: return number of states (11)
• GridWorld.actions: return lists with labels of the actions (["↑", "→", "↓", "←"])
• GridWorld.step(state, action): return possible outcomes of performing the action in a given state, as a list of triples containing
• probability: probability of the outcome
• reward: reward of the outcome
• new_state: new state of the outcome

Implement policy iteration algorithm, with --steps steps of policy evaluation/policy improvement. During policy evaluation, use the current value function and perform --iterations applications of the Bellman equation. Perform the policy evaluation synchronously (i.e., do not overwrite the current value function when computing its improvement). Assume the initial policy is “go North” and initial value function is zero.

After given number of steps and iterations, print the resulting value function and resulting policy. For example, the output after 4 steps and 4 iterations should be:

    9.15→   10.30→   11.32→   12.33↑
8.12↑             3.35←    2.58←
6.95↑    5.90←    4.66←   -4.93↓


### monte_carlo

Deadline: Nov 03, 23:59  6 points

Solve the CartPole-v1 environment environment from the OpenAI Gym using the Monte Carlo reinforcement learning algorithm.

Use the supplied cart_pole_evaluator.py module (depending on gym_evaluator.py) to interact with the discretized environment. The environment has the following methods and properties:

• states: number of states of the environment
• actions: number of actions of the environment
• episode: number of the current episode (zero-based)
• reset(start_evaluate=False) → new_state: starts a new episode
• step(action) → new_state, reward, done, info: perform the chosen action in the environment, returning the new state, obtained reward, a boolean flag indicating an end of episode, and additional environment-specific information
• render(): render current environment state

Once you finish training (which you indicate by passing start_evaluate=True to reset), your goal is to reach an average return of 490 during 100 evaluation episodes. Note that the environment prints your 100-episode average return each 10 episodes even during training.

You can start with the monte_carlo.py template, which parses several useful parameters, creates the environment and illustrates the overall usage.

During evaluation in ReCodEx, three different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 5 minutes.

Note that you must not submit gym_evaluator.py nor cart_pole_evaluator.py to ReCodEx.

### importance_sampling

Deadline: Nov 10, 23:59  4 points

Using the FrozenLake-v0 environment environment, implement Monte Carlo weighted importance sampling to estimate state value function $V$ of target policy, which uniformly chooses either action 1 (down) or action 2 (right), utilizing behaviour policy, which uniformly chooses among all four actions.

Start with the importance_sampling.py template, which creates the environment and generates episodes according to behaviour policy.

For $1000$ episodes, the output of your program should be the following:

 0.00  0.00  0.00  0.00
0.00  0.00  0.00  0.00
0.00  0.00  0.21  0.00
0.00  0.00  0.45  0.00


### q_learning

Deadline: Nov 10, 23:59  6 points

Solve the MountainCar-v0 environment environment from the OpenAI Gym using the Q-learning reinforcement learning algorithm. Note that this task does not require TensorFlow.

Use the supplied mountain_car_evaluator.py module (depending on gym_evaluator.py) to interact with the discretized environment. The environment methods and properties are described in the monte_carlo assignment. Your goal is to reach an average reward of -150 during 100 evaluation episodes.

You can start with the q_learning.py template, which parses several useful parameters, creates the environment and illustrates the overall usage. Note that setting hyperparameters of Q-learning is a bit tricky – I usualy start with a larger value of $ε$ (like 0.2 or even 0.5) an then gradually decrease it to almost zero.

During evaluation in ReCodEx, three different random seeds will be employed, and you need to reach the required return on all of them. The time limit for each test is 5 minutes.

Note that you must not submit gym_evaluator.py nor mountain_car_evaluator.py to ReCodEx.

### lunar_lander

Deadline: Nov 10, 23:59  7 points + 7 bonus

Solve the LunarLander-v2 environment environment from the OpenAI Gym. Note that this task does not require TensorFlow.

Use the supplied lunar_lander_evaluator.py module (depending on gym_evaluator.py to interact with the discretized environment. The environment methods and properties are described in the monte_carlo assignment, but include one additional method:

• expert_trajectory() → initial_state, trajectory This method generates one expert trajectory and returns a pair of initial_state and trajectory, where trajectory is a list of the tripples (action, reward, next_state). You can use this method only during training, not during evaluation.

To pass the task, you need to reach an average return of 0 during 100 evaluation episodes. During evaluation in ReCodEx, three different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 5 minutes.

The task is additionally a competition and at most 7 points will be awarded according to relative ordering of your solution performances.

You can start with the lunar_lander.py template, which parses several useful parameters, creates the environment and illustrates the overall usage.

Note that you must not submit gym_evaluator.py nor lunar_lander_evaluator.py to ReCodEx.

### q_learning_tiles

Deadline: Nov 24, 23:59  5 points

Improve the q_learning task performance on the MountainCar-v0 environment environment using linear function approximation with tile coding. Your goal is to reach an average reward of -110 during 100 evaluation episodes.

Use the mountain_car_evaluator.py module (depending on gym_evaluator.py) to interact with the discretized environment. The environment methods and properties are described in the monte_carlo assignment, with the following changes:

• The env.weights method return the number of weights of the linear function approximation.

• The state returned by the env.step method is a list containing weight indices of the current state (i.e., the feature vector of the state consists of zeros and ones, and only the indices of the ones are returned). The (action-)value function for a state is therefore approximated as a sum of the weights whose indices are returned by env.step.

The default number of tiles in tile encoding (i.e., the size of the list with weight indices) is args.tiles=8, but you can use any number you want (but the assignment is solvable with 8).

You can start with the q_learning_tiles.py template, which parses several useful parameters, creates the environment and illustrates the overall usage. Implementing Q-learning is enough to pass the assignment, even if both N-step Sarsa and Tree Backup converge a little faster.

During evaluation in ReCodEx, three different random seeds will be employed, and you need to reach the required return on all of them. The time limit for each test is 5 minutes.

Note that you must not submit gym_evaluator.py nor mountain_car_evaluator.py to ReCodEx.

### q_network

Deadline: Nov 24, 23:59  6 points

Solve the CartPole-v1 environment environment from the OpenAI Gym using Q-learning with neural network as a function approximation.

The cart_pole_evaluator.py module (depending on gym_evaluator.py) can also create a continuous environment using environment(discrete=False). The continuous environment is very similar to the discrete environment, except that the states are vectors of real-valued observations with shape environment.state_shape.

Use Q-learning with neural network as a function approximation, which for a given states returns state-action values for all actions. You can use any network architecture, but one hidden layer of 20 ReLU units is a good start.

Your goal is to reach an average return of 400 during 100 evaluation episodes.

You can start with the q_network.py template, which provides a simple network implementation in TensorFlow.

During evaluation in ReCodEx, two different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 10 minutes (so you can train in ReCodEx, but you can also pretrain your network if you like).

Note that you must not submit gym_evaluator.py nor cart_pole_evaluator.py to ReCodEx.

### car_racing

Deadline: Dec 01, 23:59  8 points + 10 bonus

The goal of this competition is to use Deep Q Networks and its improvements on a more real-world CarRacing-v0 environment environment from the OpenAI Gym.

Use the supplied car_racing_evaluator.py module (depending on gym_evaluator.py to interact with the environment. The environment is continuous and states are RGB images of size $96×96×3$, but you can downsample them even more. The actions are also continuous and consist of an array with the following three elements:

• steer in range [-1, 1]
• gas in range [0, 1]
• brake in range [0, 1]

Internally you should generate discrete actions and convert them to the required representation before the step call. Good initial action space is to use 9 actions – a Cartesian product of 3 steering actions (left/right/none) and 3 driving actions (gas/brake/none).

Nov 22: The frame skipping support was changed. The evironment supports frame skipping without rendering the skipped frames, by passing frame_skip parameter to car_racing_evaluator.environment(frame_skip=1) method – the value of frame_skip determines how many times is an action repeated.

Nov 19: The environment also supports parallel execution (use multiple CPU threads to simulate several environments in parallel during training), by providing the following two methods:

• parallel_init(num_workers) → initial_states, which initializes the given number of parallel workers and returns their environment initial states. This method can be called at most once.
• parallel_step(actions) → List[next_state, reward, done, info], which performs given action in respective environment, and return the usual information with one exception: If done=True, then next_state is already an initial state of newly started episode.

In ReCodEx, you are expected to submit an already trained model, which is evaluated on 15 different tracks with a total time limit of 15 minutes. If your average return is at least 200, you obtain 8 points. The task is also a competition and at most 10 points will be awarded according to relative ordering of your solution performances.

The car_racing.py template parses several useful parameters and creates the environment. Note that the car_racing_evaluator.py can be executed directly and in that case you can drive the car using arrows.

Note that you must not submit gym_evaluator.py nor car_racing_evaluator.py to ReCodEx.

### reinforce

Deadline: Dec 08, 23:59  5 points

Solve the CartPole-v1 environment environment from the OpenAI Gym using the REINFORCE algorithm.

The supplied cart_pole_evaluator.py module (depending on gym_evaluator.py) can create a continuous environment using environment(discrete=False). The continuous environment is very similar to the discrete environment, except that the states are vectors of real-valued observations with shape environment.state_shape.

Your goal is to reach an average return of 490 during 100 evaluation episodes.

You can start with the reinforce.py template, which provides a simple network implementation in TensorFlow.

During evaluation in ReCodEx, two different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 5 minutes.

Note that you must not submit gym_evaluator.py nor cart_pole_evaluator.py to ReCodEx.

### reinforce_baseline

Deadline: Dec 08, 23:59  5 points

This is a continuation of reinforce assignment.

Using the reinforce_baseline.py template, solve the CartPole-v1 environment environment using the REINFORCE with baseline algorithm.

Using a baseline lowers the variance of the value function gradient estimator, which allows faster training and decreases sensitivity to hyperparameter values. To reflect this effect in ReCodEx, note that the evaluation phase will automatically start after 200 episodes. Using only 200 episodes for training in this setting is probably too little for the REINFORCE algorithm, but suffices for the variant with a baseline.

Your goal is to reach an average return of 490 during 100 evaluation episodes.

During evaluation in ReCodEx, two different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 5 minutes.

Note that you must not submit gym_evaluator.py nor cart_pole_evaluator.py to ReCodEx.

### cart_pole_pixels

Deadline: Dec 08, 23:59  6 points + 6 bonus

The supplied cart_pole_pixels_evaluator.py module (depending on gym_evaluator.py) generates a pixel representation of the CartPole environment as an $80×80$ image with three channels, with each channel representing one time step (i.e., the current observation and the two previous ones).

To pass the compulsory part of the assignment, you need to reach an average return of 200 during 100 evaluation episodes. During evaluation in ReCodEx, two different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 10 minutes.

The task is additionally a competition and at most 5 points will be awarded according to relative ordering of your solution performances.

The cart_pole_pixels.py template parses several parameters and creates the environment. You are again supposed to train the model beforehand and submit only the trained neural network.

Note that you must not submit gym_evaluator.py nor cart_pole_pixels_evaluator.py to ReCodEx.

### paac

Deadline: Dec 15, 23:59  5 points

Using the paac.py template, solve the CartPole-v1 environment environment using parallel actor-critic algorithm. Use the parallel_init and parallel_step methods described in car_racing assignment.

Your goal is to reach an average return of 450 during 100 evaluation episodes.

During evaluation in ReCodEx, two different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 10 minutes.

Note that you must not submit gym_evaluator.py to ReCodEx.

### paac_continuous

Deadline: Dec 15, 23:59  6 points

Using the paac_continuous.py template, solve the MountainCarContinuous-v0 environment environment using parallel actor-critic algorithm with continuous actions.

The gym_environment now provides two additional methods:

• action_shape: returns required shape of continuous action. You can assume the actions are always an one-dimensional vector.
• action_ranges: returns a pair of vectors low, high. These denote valid ranges for the actions, so low[i]$≤$action[i]$≤$high[i].

Your goal is to reach an average return of 90 during 100 evaluation episodes.

During evaluation in ReCodEx, two different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 10 minutes.

Note that you must not submit gym_evaluator.py nor continuous_mountain_car_evaluator.py to ReCodEx.

### ddpg

Deadline: Dec 15, 23:59  7 points

Using the ddpg.py template, solve the Pendulum-v0 environment environment using deep deterministic policy gradient algorithm.

To create the evaluator, use gym_evaluator.py.GymEvaluator("Pendulum-v0"). The environment is continuous, states and actions are described at OpenAI Gym Wiki.

Your goal is to reach an average return of -200 during 100 evaluation episodes.

During evaluation in ReCodEx, two different random seeds will be employed, and you need to reach the required return on all of them. Time limit for each test is 10 minutes.

Note that you must not submit gym_evaluator.py to ReCodEx.

### walker

Deadline: Jan 05, 23:59  8 points + 10 bonus

In this exercise exploring continuous robot control, try solving the BipedalWalker-v2 environment environment from the OpenAI Gym.

To create the evaluator, use gym_evaluator.py.GymEvaluator("BipedalWalker-v2"). The environment is continuous, states and actions are described at OpenAI Gym Wiki.

In ReCodEx, you are expected to submit an already trained model, which is evaluated on 100 episodes with a total time limit of 10 minutes. If your average return is at least 100, you obtain 8 points. The task is also a competition and at most 10 points will be awarded according to relative ordering of your solution performances.

You can start with the ddpg.py template, only set args.env to BipedalWalker-v2.

Note that you must not submit gym_evaluator.py to ReCodEx.

### walker_hardcore

Deadline: Jan 05, 23:59  10 bonus

As an extesnion of the walker assignment, try solving the BipedalWalkerHardcore-v2 environment environment from the OpenAI Gym.

The task is a competition only and at most 10 points will be awarded according to relative ordering of your solution performances. In ReCodEx, your solution will be evaluated on 100 episodes with a total time limit of 10 minutes. If your average return is at least 0, ReCodEx shows the solution as correct.

You can start with the ddpg.py template, only set args.env to BipedalWalkerHardcore-v2.

Note that you must not submit gym_evaluator.py to ReCodEx.

### az_quiz

Deadline: Jan 05, 23:59  10 points + 10 bonus

In this competition assignment, use Monte Carlo Tree Search to learn an agent for a simplified version of AZ-kvíz. In our version, the agent does not have to answer questions and we assume that all answers are correct.

The game itself is implemented in the az_quiz.py module, using randomized=False constructor argument.

The evaluation in ReCodEx should be implemented by importing a module az_quiz_evaluator_recodex and calling its evaluate function. The argument this functions is an object providing a method play which given an AZ-kvíz instance returns the chosen move. The illustration of the interface is in the az_quiz_evaluator_recodex.py module, a simple random player implementing the interface is the az_quiz_player_random.py.

Your solution in ReCodEx is automatically evaluated against a very simple heuristic az_quiz_player_simple_heuristic.py, playing 50 games as a starting player and 50 games as a non-starting player. The time limit for the games is 15 minutes and you should see the win rate directly in ReCodEx. If you achieve at least 75%, you will pass the assignment.

The final competition evaluation will be performed after the deadline by a round-robin tournament.

Note that az_quiz_evaluator.py can be used to evaluate any two given implementations and there are two interactive players available, az_quiz_player_interactive_mouse.py and az_quiz_player_interactive_keyboard.py.

For inspiration, use the official pseudocode for AlphaZero. However, note that there is an error on line 258, and the correct version should look like

value_score = 1 - child.value()


Note that you must not submit az_quiz.py nor az_quiz_evaluator_recodex.py to ReCodEx.

### az_quiz_randomized

Deadline: Jan 05, 23:59  10 bonus

Extend the az_quiz assignment to handle the possibility of wrong answers. Therefore, when choosing a field, the agent might answer incorrectly.

To instantiate this randomized game variant, pass randomized=True to the AZQuiz class of az_quiz.py.

The Monte Carlo Tree Search has to be slightly modified to handle stochastic MDP. The information about distribution of possible next states is provided by the AZQuiz.all_moves method, which returns a list of (probability, az_quiz_instance) next states (in our environment, there are always two possible next states).

Note that you must not submit az_quiz.py nor az_quiz_evaluator_recodex.py to ReCodEx.

### Requirements

To pass the practicals, you need to obtain at least 80 points, excluding the bonus points. Note that up to 40 points above 80 will be transfered to the exam.

To pass the exam, you need to obtain at least 60, 75 and 90 out of 100-point exam, to obtain grades 3, 2 and 1, respectively. The exam consists of five 20-point questions and in addition, you can get at most 40 surplus points from the practicals and at most 10 points for community work (i.e., fixing slides or reporting issues).

### Exam Questions

Please note that this list is still under construction!

• General RL Settings, Value Iteration Define reinforcement learning as a Markov Decision Process, define a policy, value function and an action-value function (and show how value and action-value functions can be computed from one another). Then, define optimal value and action-value function, and show, how optimal value function can be computed using Bellman backup operator, i.e., the value iteration algorithm (including a proof of convergence).

• General RL Settings, Policy Iteration Define reinforcement learning as a Markov Decision Process, define a policy, value function and an action-value function (and show how value and action-value functions can be computed from one another). Then, define optimal value and action-value function, and show, how optimal policy can be computed using policy iteration algorithm (ideally including proofs).

• TD Methods Describe temporal difference methods and formulate Sarsa, Q-learning, Expected Sarsa, Double Q-learning and $n$-step Sarsa in tabular settings.

• Off-policy Methods Describe difference between on-policy and off-policy methods, and show an off-policy variant of Monte Carlo algorithm in tabular settings, both with ordinary and weighted importance sampling. Then describe Expected Sarsa as an off-policy algorithm not using importance sampling. Finally, describe off-policy $n$-step Sarsa and Tree Backup algorithms.

• Function Approximation Assuming function approximation, define the usual mean squared value error and describe gradient Monte Carlo and Semi-gradient TD algorithms. Then show how off-policy methods in function approximation settings may diverge. Finally, sketch Deep Q Network architecture, especially the experience replay and target network.

• DQN Describe Deep Q Network, and especially experience replay, target network and reward clipping tricks. Then, describe at least three improvements present in Rainbow algorithm (i.e., something of DDQN, prioritized replay, duelling architecture, noisy nets and distributional RL).

• Policy Gradient Methods, REINFORCE Describe policy gradient methods, prove policy gradient theorem, and describe REINFORCE, REINFORCE with baseline (including the proof of the baseline).

• Policy Gradient Methods, PAAC Describe policy gradient methods, prove policy gradient theorem, and describe Parallel advantage actor-critic (PAAC) algorithm.

• Gradient Methods with Continuous Actions, DDPG Show how continuous actions can be incorporated in policy gradient algorithms (i.e., in a REINFORCE algorithm, without proving the policy gradient theorem). Then formulate and prove deterministic policy gradient theorem. Finally, sketch the DDPG algorithm.

• Gradient Methods with Continuous Actions, TD3 Formulate and prove deterministic policy gradient theorem. Then, describe the DDPG and TD3 algorithms.

• AlphaZero Describe the algorithm used by AlphaZero – Monte Carlo tree search, overall neural network architecture, and training and inference procedures.

• V-trace and PopArt Normalization Describe the V-trace algorithm and sketch population-based training used in the IMPALA algorithm. Then, show how the rewards can be normalized using the PopArt normalization approach.