The current state-of-the-art in artificial intelligence is impressive, especially in terms of mastery of language, but not so much in terms of mathematical reasoning. What could be missing? Can we learn something useful about that gap from how the brains of mathematicians go about their craft? This essay builds on the idea that current deep learning mostly succeeds at system 1 abilities -- which correspond to our intuition and habitual behaviors -- but still lacks something important regarding system 2 abilities -- which include reasoning and robust uncertainty estimation. It takes an information-theoretical posture to ask questions about what constitutes an interesting mathematical statement, which could guide future work in crafting an AI mathematician. The focus is not on proving a given theorem but on discovering new and interesting conjectures. The central hypothesis is that a desirable body of theorems better summarizes the set of all provable statements, for example by having a small description length while at the same time being close (in terms of number of derivation steps) to many provable statements.

Current model-based reinforcement learning (MBRL) agents struggle with long-term dependencies. This limits their ability to effectively solve tasks involving extended time gaps between actions and outcomes, or tasks demanding the recalling of distant observations to inform current actions. To improve temporal coherence, we integrate a new family of state space models (SSMs) in world models of MBRL agents to present a new method, Recall to Imagine (R2I). This integration aims to enhance both long-term memory and long-horizon credit assignment. Through a diverse set of illustrative tasks, we systematically demonstrate that R2I not only establishes a new state-of-the-art for challenging memory and credit assignment RL tasks, such as BSuite and POPGym, but also showcases superhuman performance in the complex memory domain of Memory Maze. At the same time, it upholds comparable performance in classic RL tasks, such as Atari and DMC, suggesting the generality of our method. We also show that R2I is faster than the state-of-the-art MBRL method, DreamerV3, resulting in faster wall-time convergence.

Effective action abstraction is crucial in tackling challenges associated with large action spaces in Imperfect Information Extensive-Form Games (IIEFGs). However, due to the vast state space and computational complexity in IIEFGs, existing methods often rely on fixed abstractions, resulting in sub-optimal performance. In response, we introduce RL-CFR, a novel reinforcement learning (RL) approach for dynamic action abstraction. RL-CFR builds upon our innovative Markov Decision Process (MDP) formulation, with states corresponding to public information and actions represented as feature vectors indicating specific action abstractions. The reward is defined as the expected payoff difference between the selected and default action abstractions. RL-CFR constructs a game tree with RL-guided action abstractions and utilizes counterfactual regret minimization (CFR) for strategy derivation. Impressively, it can be trained from scratch, achieving higher expected payoff without increased CFR solving time. In experiments on Heads-up No-limit Texas Hold'em, RL-CFR outperforms ReBeL's replication and Slumbot, demonstrating significant win-rate margins of $64\pm 11$ and $84\pm 17$ mbb/hand, respectively.

Humans perceive the world through multiple senses, enabling them to create a comprehensive representation of their surroundings and to generalize information across domains. For instance, when a textual description of a scene is given, humans can mentally visualize it. In fields like robotics and Reinforcement Learning (RL), agents can also access information about the environment through multiple sensors; yet redundancy and complementarity between sensors is difficult to exploit as a source of robustness (e.g. against sensor failure) or generalization (e.g. transfer across domains). Prior research demonstrated that a robust and flexible multimodal representation can be efficiently constructed based on the cognitive science notion of a 'Global Workspace': a unique representation trained to combine information across modalities, and to broadcast its signal back to each modality. Here, we explore whether such a brain-inspired multimodal representation could be advantageous for RL agents. First, we train a 'Global Workspace' to exploit information collected about the environment via two input modalities (a visual input, or an attribute vector representing the state of the agent and/or its environment). Then, we train a RL agent policy using this frozen Global Workspace. In two distinct environments and tasks, our results reveal the model's ability to perform zero-shot cross-modal transfer between input modalities, i.e. to apply to image inputs a policy previously trained on attribute vectors (and vice-versa), without additional training or fine-tuning. Variants and ablations of the full Global Workspace (including a CLIP-like multimodal representation trained via contrastive learning) did not display the same generalization abilities.

Load frequency control (LFC) is widely employed in power systems to stabilize frequency fluctuation and guarantee power quality. However, most existing LFC methods rely on accurate power system modeling and usually ignore the nonlinear characteristics of the system, limiting controllers' performance. To solve these problems, this paper proposes a model-free LFC method for nonlinear power systems based on deep deterministic policy gradient (DDPG) framework. The proposed method establishes an emulator network to emulate power system dynamics. After defining the action-value function, the emulator network is applied for control actions evaluation instead of the critic network. Then the actor network controller is effectively optimized by estimating the policy gradient based on zeroth-order optimization (ZOO) and backpropagation algorithm. Simulation results and corresponding comparisons demonstrate the designed controller can generate appropriate control actions and has strong adaptability for nonlinear power systems.

Evolutionary algorithms, such as Differential Evolution, excel in solving real-parameter optimization challenges. However, the effectiveness of a single algorithm varies across different problem instances, necessitating considerable efforts in algorithm selection or configuration. This paper aims to address the limitation by leveraging the complementary strengths of a group of algorithms and dynamically scheduling them throughout the optimization progress for specific problems. We propose a deep reinforcement learning-based dynamic algorithm selection framework to accomplish this task. Our approach models the dynamic algorithm selection a Markov Decision Process, training an agent in a policy gradient manner to select the most suitable algorithm according to the features observed during the optimization process. To empower the agent with the necessary information, our framework incorporates a thoughtful design of landscape and algorithmic features. Meanwhile, we employ a sophisticated deep neural network model to infer the optimal action, ensuring informed algorithm selections. Additionally, an algorithm context restoration mechanism is embedded to facilitate smooth switching among different algorithms. These mechanisms together enable our framework to seamlessly select and switch algorithms in a dynamic online fashion. Notably, the proposed framework is simple and generic, offering potential improvements across a broad spectrum of evolutionary algorithms. As a proof-of-principle study, we apply this framework to a group of Differential Evolution algorithms. The experimental results showcase the remarkable effectiveness of the proposed framework, not only enhancing the overall optimization performance but also demonstrating favorable generalization ability across different problem classes.

Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time control problems, is unable to directly estimate the generalization error of the Bellman optimal loss and require a boundedness assumption. Our work focuses on continuous-time control problems and proposes a method that is applicable to all such problems where the transition function satisfies semi-group and Lipschitz properties. Under this method, we can directly analyze the \emph{a priori} generalization error of the Bellman optimal loss. The core of this method lies in two transformations of the loss function. To complete the transformation, we propose a decomposition method for the maximum operator. Additionally, this analysis method does not require a boundedness assumption. Finally, we obtain an \emph{a priori} generalization error without the curse of dimensionality.

In cooperative multi-agent reinforcement learning (MARL), agents aim to achieve a common goal, such as defeating enemies or scoring a goal. Existing MARL algorithms are effective but still require significant learning time and often get trapped in local optima by complex tasks, subsequently failing to discover a goal-reaching policy. To address this, we introduce Efficient episodic Memory Utilization (EMU) for MARL, with two primary objectives: (a) accelerating reinforcement learning by leveraging semantically coherent memory from an episodic buffer and (b) selectively promoting desirable transitions to prevent local convergence. To achieve (a), EMU incorporates a trainable encoder/decoder structure alongside MARL, creating coherent memory embeddings that facilitate exploratory memory recall. To achieve (b), EMU introduces a novel reward structure called episodic incentive based on the desirability of states. This reward improves the TD target in Q-learning and acts as an additional incentive for desirable transitions. We provide theoretical support for the proposed incentive and demonstrate the effectiveness of EMU compared to conventional episodic control. The proposed method is evaluated in StarCraft II and Google Research Football, and empirical results indicate further performance improvement over state-of-the-art methods. Our code is available at: https://github.com/HyunghoNa/EMU.

A significant hurdle in the noisy intermediate-scale quantum (NISQ) era is identifying functional quantum circuits. These circuits must also adhere to the constraints imposed by current quantum hardware limitations. Variational quantum algorithms (VQAs), a class of quantum-classical optimization algorithms, were developed to address these challenges in the currently available quantum devices. However, the overall performance of VQAs depends on the initialization strategy of the variational circuit, the structure of the circuit (also known as ansatz), and the configuration of the cost function. Focusing on the structure of the circuit, in this thesis, we improve the performance of VQAs by automating the search for an optimal structure for the variational circuits using reinforcement learning (RL). Within the thesis, the optimality of a circuit is determined by evaluating its depth, the overall count of gates and parameters, and its accuracy in solving the given problem. The task of automating the search for optimal quantum circuits is known as quantum architecture search (QAS). The majority of research in QAS is primarily focused on a noiseless scenario. Yet, the impact of noise on the QAS remains inadequately explored. In this thesis, we tackle the issue by introducing a tensor-based quantum circuit encoding, restrictions on environment dynamics to explore the search space of possible circuits efficiently, an episode halting scheme to steer the agent to find shorter circuits, a double deep Q-network (DDQN) with an $\epsilon$-greedy policy for better stability. The numerical experiments on noiseless and noisy quantum hardware show that in dealing with various VQAs, our RL-based QAS outperforms existing QAS. Meanwhile, the methods we propose in the thesis can be readily adapted to address a wide range of other VQAs.

Reinforcement learning with human feedback (RLHF) is an emerging paradigm to align models with human preferences. Typically, RLHF aggregates preferences from multiple individuals who have diverse viewpoints that may conflict with each other. Our work \textit{initiates} the theoretical study of multi-party RLHF that explicitly models the diverse preferences of multiple individuals. We show how traditional RLHF approaches can fail since learning a single reward function cannot capture and balance the preferences of multiple individuals. To overcome such limitations, we incorporate meta-learning to learn multiple preferences and adopt different social welfare functions to aggregate the preferences across multiple parties. We focus on the offline learning setting and establish sample complexity bounds, along with efficiency and fairness guarantees, for optimizing diverse social welfare functions such as Nash, Utilitarian, and Leximin welfare functions. Our results show a separation between the sample complexities of multi-party RLHF and traditional single-party RLHF. Furthermore, we consider a reward-free setting, where each individual's preference is no longer consistent with a reward model, and give pessimistic variants of the von Neumann Winner based on offline preference data. Taken together, our work showcases the advantage of multi-party RLHF but also highlights its more demanding statistical complexity.