# Reinforcement Learning

### On "solving" Montezuma's Revenge – Arthur Juliani – Medium

In recent weeks DeepMind and OpenAI have each shared that they developed agents which can learn to complete the first level of the Atari 2600 game Montezuma's Revenge. These claims are important because Montezuma's Revenge is important. Unlike the vast majority of the games in the Arcade Learning Environment (ALE), which are now easily solved at superhuman level by learned agents, Montezuma's Revenge has been hitherto unsolved by Deep Reinforcement Learning methods and was thought by some to be unsolvable for years to come. What distinguishes Montezuma's Revenge from other games in the ALE is its relatively sparse rewards. For those unfamiliar, that means that the agent only receives reward signals after completing specific series of actions over extended periods of time.

### What is reinforcement learning? The complete guide deepsense.ai

With an estimated market size of 7.35 billion US dollars, artificial intelligence is growing by leaps and bounds. McKinsey predicts that AI techniques (including deep learning and reinforcement learning) have the potential to create between $3.5T and$5.8T in value annually across nine business functions in 19 industries. Although machine learning is seen as a monolith, this cutting-edge technology is diversified, with various sub-types including machine learning, deep learning, and the state-of-art technology of deep reinforcement learning. Reinforcement learning is the training of machine learning models to make a sequence of decisions. The agent learns to achieve a goal in an uncertain, potentially complex environment.

### Why temporal difference (TD) method has lower variance than Monte Carlo method?

This question might be a little trivial. However, I had a hard time understanding it or finding some formal proof for it. In many papers, it is being said that for estimating the value function, one of the advantages of using temporal difference methods over the Monte Carlo methods in reinforcement learning is that they have a lower variance for computing value function. Up to now, I was not able to find any formal proof for this. Moreover, it is also being said that the Monte Carlo method is less biased when compared with TD methods.

### Visual Reinforcement Learning with Imagined Goals

For an autonomous agent to fulfill a wide range of user-specified goals at test time, it must be able to learn broadly applicable and general-purpose skill repertoires. Furthermore, to provide the requisite level of generality, these skills must handle raw sensory input such as images. In this paper, we propose an algorithm that acquires such general-purpose skills by combining unsupervised representation learning and reinforcement learning of goal-conditioned policies. Since the particular goals that might be required at test-time are not known in advance, the agent performs a self-supervised "practice" phase where it imagines goals and attempts to achieve them. We learn a visual representation with three distinct purposes: sampling goals for self-supervised practice, providing a structured transformation of raw sensory inputs, and computing a reward signal for goal reaching. We also propose a retroactive goal relabeling scheme to further improve the sample-efficiency of our method. Our off-policy algorithm is efficient enough to learn policies that operate on raw image observations and goals for a real-world robotic system, and substantially outperforms prior techniques.

### Will it Blend? Composing Value Functions in Reinforcement Learning

An important property for lifelong-learning agents is the ability to combine existing skills to solve unseen tasks. In general, however, it is unclear how to compose skills in a principled way. We provide a "recipe" for optimal value function composition in entropy-regularised reinforcement learning (RL) and then extend this to the standard RL setting. Composition is demonstrated in a video game environment, where an agent with an existing library of policies is able to solve new tasks without the need for further learning.

### Transform Your Business Process Into a Game and Let an AI Become Best At It - insideBIGDATA

In this special guest feature, Eliya Elon, Director of Product and Business Development at Razor Labs, discusses a new technology that is starting to trickle from the purely theoretical academic world to the business world, one that aligns with your company objectives, that draws a clear line between your business question and the insights generated. This new technology is called Deep Reinforcement-Learning, and it is gaining significant success in different use-cases. Eliya is the VP of Product and strategic partnerships at Razor Labs. He is an experienced tech entrepreneur, selling his last AI company in 2017. Since joining Razor Labs he is focused on creating AI products that bridge the multi-dimensional gap of business needs, user experience, and academic research, hopefully at scale.

### Algorithmic Framework for Model-based Reinforcement Learning with Theoretical Guarantees

While model-based reinforcement learning has empirically been shown to significantly reduce the sample complexity that hinders model-free RL, the theoretical understanding of such methods has been rather limited. In this paper, we introduce a novel algorithmic framework for designing and analyzing model-based RL algorithms with theoretical guarantees, and a practical algorithm Optimistic Lower Bounds Optimization (OLBO). In particular, we derive a theoretical guarantee of monotone improvement for model-based RL with our framework. We iteratively build a lower bound of the expected reward based on the estimated dynamical model and sample trajectories, and maximize it jointly over the policy and the model. Assuming the optimization in each iteration succeeds, the expected reward is guaranteed to improve. The framework also incorporates an optimism-driven perspective, and reveals the intrinsic measure for the model prediction error. Preliminary simulations demonstrate that our approach outperforms the standard baselines on continuous control benchmark tasks.

### Is Q-learning Provably Efficient?

Model-free reinforcement learning (RL) algorithms, such as Q-learning, directly parameterize and update value functions or policies without explicitly modeling the environment. They are typically simpler, more flexible to use, and thus more prevalent in modern deep RL than model-based approaches. However, empirical work has suggested that model-free algorithms may require more samples to learn [Deisenroth and Rasmussen 2011, Schulman et al. 2015]. The theoretical question of "whether model-free algorithms can be made sample efficient" is one of the most fundamental questions in RL, and remains unsolved even in the basic scenario with finitely many states and actions. We prove that, in an episodic MDP setting, Q-learning with UCB exploration achieves regret $\tilde{O}(\sqrt{H^3 SAT})$, where $S$ and $A$ are the numbers of states and actions, $H$ is the number of steps per episode, and $T$ is the total number of steps. This sample efficiency matches the optimal regret that can be achieved by any model-based approach, up to a single $\sqrt{H}$ factor. To the best of our knowledge, this is the first analysis in the model-free setting that establishes $\sqrt{T}$ regret without requiring access to a "simulator."

### Generalized deterministic policy gradient algorithms

We study a setting of reinforcement learning, where the state transition is a convex combination of a stochastic continuous function and a deterministic discontinuous function. Such a setting include as a special case the stochastic state transition setting, namely the setting of deterministic policy gradient (DPG). We introduce a theoretical technique to prove the existence of the policy gradient in this generalized setting. Using this technique, we prove that the deterministic policy gradient indeed exists for a certain set of discount factors, and further prove two conditions that guarantee the existence for all discount factors. We then derive a closed form of the policy gradient whenever exists. Interestingly, the form of the policy gradient in such setting is equivalent to that in DPG. Furthermore, to overcome the challenge of high sample complexity of DPG in this setting, we propose the Generalized Deterministic Policy Gradient (GDPG) algorithm. The main innovation of the algorithm is to optimize a weighted objective of the original Markov decision process (MDP) and an augmented MDP that simplifies the original one, and serves as its lower bound. To solve the augmented MDP, we make use of the model-based methods which enable fast convergence. We finally conduct extensive experiments comparing GDPG with state-of-the-art methods on several standard benchmarks. Results demonstrate that GDPG substantially outperforms other baselines in terms of both convergence and long-term rewards.

### Temporal Difference Learning with Neural Networks - Study of the Leakage Propagation Problem

Temporal-Difference learning (TD) [Sutton, 1988] with function approximation can converge to solutions that are worse than those obtained by Monte-Carlo regression, even in the simple case of on-policy evaluation. To increase our understanding of the problem, we investigate the issue of approximation errors in areas of sharp discontinuities of the value function being further propagated by bootstrap updates. We show empirical evidence of this leakage propagation, and show analytically that it must occur, in a simple Markov chain, when function approximation errors are present. For reversible policies, the result can be interpreted as the tension between two terms of the loss function that TD minimises, as recently described by [Ollivier, 2018]. We show that the upper bounds from [Tsitsiklis and Van Roy, 1997] hold, but they do not imply that leakage propagation occurs and under what conditions. Finally, we test whether the problem could be mitigated with a better state representation, and whether it can be learned in an unsupervised manner, without rewards or privileged information.