We will incorporate the suggestions. More details were provided in Appendix B.1, especially We will add these pointers and more descriptions in main text to clarify our algorithm. We will make the connection between DTSIL and prior works more clear, especially for imitation learning part. Pseudocode for organizing clusters was in Appendix A.3. DTSIL+EXP without SL performs worse on Montezuma's Revenge Assume agent's location in state embeddings is normalized to We will add this comparison and more discussions about off-policy and model-based exploration methods.

We will incorporate the suggestions. More details were provided in Appendix B.1, especially We will add these pointers and more descriptions in main text to clarify our algorithm. We will make the connection between DTSIL and prior works more clear, especially for imitation learning part. Pseudocode for organizing clusters was in Appendix A.3. DTSIL+EXP without SL performs worse on Montezuma's Revenge Assume agent's location in state embeddings is normalized to We will add this comparison and more discussions about off-policy and model-based exploration methods.

We have devised an artificial intelligence algorithm with machine reinforcement learning (Q-learning) to construct remarkable entangled states with 4 qubits. This way, the algorithm is able to generate representative states for some of the 49 true SLOCC classes of the four-qubit entanglement states. In particular, it is possible to reach at least one true SLOCC class for each of the nine entanglement families. The quantum circuits synthesized by the algorithm may be useful for the experimental realization of these important classes of entangled states and to draw conclusions about the intrinsic properties of our universe. We introduce a graphical tool called the state-link graph (SLG) to represent the construction of the Quality matrix (Q-matrix) used by the algorithm to build a given objective state belonging to the corresponding entanglement class. This allows us to discover the necessary connections between specific entanglement features and the role of certain quantum gates that the algorithm needs to include in the quantum gate set of actions. The quantum circuits found are optimal by construction with respect to the quantum gate-set chosen. These SLGs make the algorithm simple, intuitive and a useful resource for the automated construction of entangled states with a low number of qubits.

We discuss prototype formation in the Hopfield network. Typically, Hebbian learning with highly correlated states leads to degraded memory performance. We show this type of learning can lead to prototype formation, where unlearned states emerge as representatives of large correlated subsets of states, alleviating capacity woes. This process has similarities to prototype learning in human cognition. We provide a substantial literature review of prototype learning in associative memories, covering contributions from psychology, statistical physics, and computer science. We analyze prototype formation from a theoretical perspective and derive a stability condition for these states based on the number of examples of the prototype presented for learning, the noise in those examples, and the number of non-example states presented. The stability condition is used to construct a probability of stability for a prototype state as the factors of stability change. We also note similarities to traditional network analysis, allowing us to find a prototype capacity. We corroborate these expectations of prototype formation with experiments using a simple Hopfield network with standard Hebbian learning. We extend our experiments to a Hopfield network trained on data with multiple prototypes and find the network is capable of stabilizing multiple prototypes concurrently. We measure the basins of attraction of the multiple prototype states, finding attractor strength grows with the number of examples and the agreement of examples. We link the stability and dominance of prototype states to the energy profile of these states, particularly when comparing the profile shape to target states or other spurious states.

Kernel-based reinforcement-learning (KBRL) is a method for learning a decision policy from a set of sample transitions which stands out for its strong theoretical guarantees. However, the size of the approximator grows with the number of transitions, which makes the approach impractical for large problems. In this paper we introduce a novel algorithm to improve the scalability of KBRL. We resort to a special decomposition of a transition matrix, called stochastic factorization, to fix the size of the approximator while at the same time incorporating all the information contained in the data. The resulting algorithm, kernel-based stochastic factorization (KBSF), is much faster but still converges to a unique solution. We derive a theoretical upper bound for the distance between the value functions computed by KBRL and KBSF. The effectiveness of our method is illustrated with computational experiments on four reinforcement-learning problems, including a difficult task in which the goal is to learn a neurostimulation policy to suppress the occurrence of seizures in epileptic rat brains. We empirically demonstrate that the proposed approach is able to compress the information contained in KBRL's model. Also, on the tasks studied, KBSF outperforms two of the most prominent reinforcement-learning algorithms, namely least-squares policy iteration and fitted Q-iteration.

Kernel-based stochastic factorization (KBSF) is an algorithm for solving reinforcement learning tasks with continuous state spaces which builds a Markov decision process (MDP) based on a set of sample transitions. What sets KBSF apart from other kernel-based approaches is the fact that the size of its MDP is independent of the number of transitions, which makes it possible to control the trade-off between the quality of the resulting approximation and the associated computational cost. However, KBSF's memory usage grows linearly with the number of transitions, precluding its application in scenarios where a large amount of data must be processed. In this paper we show that it is possible to construct KBSF's MDP in a fully incremental way, thus freeing the space complexity of this algorithm from its dependence on the number of sample transitions. The incremental version of KBSF is able to process an arbitrary amount of data, which results in a model-based reinforcement learning algorithm that can be used to solve continuous MDPs in both off-line and on-line regimes. We present theoretical results showing that KBSF can approximate the value function that would be computed by conventional kernel-based learning with arbitrary precision. We empirically demonstrate the effectiveness of the proposed algorithm in the challenging threepole balancing task, in which the ability to process a large number of transitions is crucial for success.

In this work, we propose KeRNS: an algorithm for episodic reinforcement learning in non-stationary Markov Decision Processes (MDPs) whose state-action set is endowed with a metric. Using a non-parametric model of the MDP built with time-dependent kernels, we prove a regret bound that scales with the covering dimension of the state-action space and the total variation of the MDP with time, which quantifies its level of non-stationarity. Our method generalizes previous approaches based on sliding windows and exponential discounting used to handle changing environments. We further propose a practical implementation of KeRNS, we analyze its regret and validate it experimentally.

Kernel-based reinforcement learning (KBRL) stands out among reinforcement learning algorithms for its strong theoretical guarantees. By casting the learning problem as a local kernel approximation, KBRL provides a way of computing a decision policy which is statistically consistent and converges to a unique solution. Unfortunately, the model constructed by KBRL grows with the number of sample transitions, resulting in a computational cost that precludes its application to large-scale or on-line domains. In this paper we introduce an algorithm that turns KBRL into a practical reinforcement learning tool. Kernel-based stochastic factorization (KBSF) builds on a simple idea: when a transition matrix is represented as the product of two stochastic matrices, one can swap the factors of the multiplication to obtain another transition matrix, potentially much smaller, which retains some fundamental properties of its precursor. KBSF exploits such an insight to compress the information contained in KBRL's model into an approximator of fixed size. This makes it possible to build an approximation that takes into account both the difficulty of the problem and the associated computational cost. KBSF's computational complexity is linear in the number of sample transitions, which is the best one can do without discarding data. Moreover, the algorithm's simple mechanics allow for a fully incremental implementation that makes the amount of memory used independent of the number of sample transitions. The result is a kernel-based reinforcement learning algorithm that can be applied to large-scale problems in both off-line and on-line regimes. We derive upper bounds for the distance between the value functions computed by KBRL and KBSF using the same data. We also illustrate the potential of our algorithm in an extensive empirical study in which KBSF is applied to difficult tasks based on real-world data.

Kernel-based reinforcement learning (KBRL) is a popular approach to learning non-parametric value function approximations. In this paper, we present structured KBRL, a paradigm for kernel-based RL that allows for modeling independencies in the transition and reward models of problems. Real-world problems often exhibit this structure and can be solved more efficiently when it is modeled. We make three contributions. First, we motivate our work, define a structured backup operator, and prove that it is a contraction. Second, we show how to evaluate our operator efficiently. Our analysis reveals that the fixed point of the operator is the optimal value function in a special factored MDP. Finally, we evaluate our method on a synthetic problem and compare it to two KBRL baselines. In most experiments, we learn better policies than the baselines from an order of magnitude less training data.

Kernel-based stochastic factorization (KBSF) is an algorithm for solving reinforcement learningtasks with continuous state spaces which builds a Markov decision process (MDP) based on a set of sample transitions. What sets KBSF apart from other kernel-based approaches is the fact that the size of its MDP is independent ofthe number of transitions, which makes it possible to control the tradeoff between the quality of the resulting approximation and the associated computational cost.However, KBSF's memory usage grows linearly with the number of transitions, precluding its application in scenarios where a large amount of data must be processed. In this paper we show that it is possible to construct KBSF's MDP in a fully incremental way, thus freeing the space complexity of this algorithm fromits dependence on the number of sample transitions. The incremental version of KBSF is able to process an arbitrary amount of data, which results in a model-based reinforcement learning algorithm that can be used to solve continuous MDPsin both off-line and online regimes. We present theoretical results showing that KBSF can approximate the value function that would be computed by conventional kernel-based learning with arbitrary precision. We empirically demonstrate the effectiveness of the proposed algorithm in the challenging threepole balancingtask, in which the ability to process a large number of transitions is crucial for success.