We introduce the forward-backward (FB) representation of the dynamics of a reward-free Markov decision process. It provides explicit near-optimal policies for any reward specified a posteriori. During an unsupervised phase, we use rewardfree interactions with the environment to learn two representations via off-the-shelf deep learning methods and temporal difference (TD) learning. In the test phase, a reward representation is estimated either from reward observations or an explicit reward description (e.g., a target state). The optimal policy for that reward is directly obtained from these representations, with no planning.

We provide improved gap-dependent regret bounds for reinforcement learning in finite episodic Markov decision processes. Compared to prior work, our bounds depend on alternative definitions of gaps. These definitions are based on the insight that, in order to achieve a favorable regret, an algorithm does not need to learn how to behave optimally in states that are not reached by an optimal policy. We prove tighter upper regret bounds for optimistic algorithms and accompany them with new information-theoretic lower bounds for a large class of MDPs. Our results show that optimistic algorithms can not achieve the information-theoretic lower bounds even in deterministic MDPs unless there is a unique optimal policy.

We introduce the forward-backward (FB) representation of the dynamics of a reward-free Markov decision process. It provides explicit near-optimal policies for any reward specified a posteriori. During an unsupervised phase, we use rewardfree interactions with the environment to learn two representations via off-the-shelf deep learning methods and temporal difference (TD) learning. In the test phase, a reward representation is estimated either from reward observations or an explicit reward description (e.g., a target state). The optimal policy for that reward is directly obtained from these representations, with no planning.

We provide improved gap-dependent regret bounds for reinforcement learning in finite episodic Markov decision processes. Compared to prior work, our bounds depend on alternative definitions of gaps. These definitions are based on the insight that, in order to achieve a favorable regret, an algorithm does not need to learn how to behave optimally in states that are not reached by an optimal policy. We prove tighter upper regret bounds for optimistic algorithms and accompany them with new information-theoretic lower bounds for a large class of MDPs. Our results show that optimistic algorithms can not achieve the information-theoretic lower bounds even in deterministic MDPs unless there is a unique optimal policy.

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanical approach to analyze sparse equation discovery algorithms, which typically balance data fit and parsimony through a trial-and-error selection of hyperparameters. In this framework, statistical mechanics offers tools to analyze the interplay between complexity and fitness, in analogy to that done between entropy and energy. To establish this analogy, we define the optimization procedure as a two-level Bayesian inference problem that separates variable selection from coefficient values and enables the computation of the posterior parameter distribution in closed form. A key advantage of employing statistical mechanical concepts, such as free energy and the partition function, is in the quantification of uncertainty, especially in in the low-data limit; frequently encountered in real-world applications. As the data volume increases, our approach mirrors the thermodynamic limit, leading to distinct sparsity- and noise-induced phase transitions that delineate correct from incorrect identification. This perspective of sparse equation discovery, is versatile and can be adapted to various other equation discovery algorithms.

In a basketball game, scoring efficiency holds significant importance due to the numerous offensive possessions per game. Enhancing scoring efficiency necessitates effective collaboration among players with diverse playing styles. In previous studies, basketball lineups have been analyzed, but their playing style compatibility has not been quantitatively examined. The purpose of this study is to analyze more specifically the impact of playing style compatibility on scoring efficiency, focusing only on offense. This study employs two methods to capture the playing styles of players on offense: shooting style clustering using tracking data, and offensive role clustering based on annotated playtypes and advanced statistics. For the former, interpretable hand-crafted shot features and Wasserstein distances between shooting style distributions were utilized. For the latter, soft clustering was applied to playtype data for the first time. Subsequently, based on the lineup information derived from these two clusterings, machine learning models Bayesian models that predict statistics representing scoring efficiency were trained and interpreted. These approaches provide insights into which combinations of five players tend to be effective and which combinations of two players tend to produce good effects.

What constitutes human creativity, and is it possible for computers to exhibit genuine creativity? We argue that achieving human-level intelligence in computers, or so-called Artificial General Intelligence, necessitates attaining also human-level creativity. We contribute to this discussion by developing a statistical representation of human creativity, incorporating prior insights from stochastic theory, psychology, philosophy, neuroscience, and chaos theory. This highlights the stochastic nature of the human creative process, which includes both a bias guided, random proposal step, and an evaluation step depending on a flexible or transformable bias structure. The acquired representation of human creativity is subsequently used to assess the creativity levels of various contemporary AI systems. Our analysis includes modern AI algorithms such as reinforcement learning, diffusion models, and large language models, addressing to what extent they measure up to human level creativity. We conclude that these technologies currently lack the capability for autonomous creative action at a human level.

Recently, there has been a surge of interest in incorporating neural networks into particle filters, e.g. differentiable particle filters, to perform joint sequential state estimation and model learning for non-linear non-Gaussian state-space models in complex environments. Existing differentiable particle filters are mostly constructed with vanilla neural networks that do not allow density estimation. As a result, they are either restricted to a bootstrap particle filtering framework or employ predefined distribution families (e.g. Gaussian distributions), limiting their performance in more complex real-world scenarios. In this paper we present a differentiable particle filtering framework that uses (conditional) normalising flows to build its dynamic model, proposal distribution, and measurement model. This not only enables valid probability densities but also allows the proposed method to adaptively learn these modules in a flexible way, without being restricted to predefined distribution families. We derive the theoretical properties of the proposed filters and evaluate the proposed normalising flow-based differentiable particle filters' performance through a series of numerical experiments.

We investigate the replay buffer in rehearsal-based approaches for graph continual learning (GCL) methods. Existing rehearsal-based GCL methods select the most representative nodes for each class and store them in a replay buffer for later use in training subsequent tasks. However, we discovered that considering only the class representativeness of each replayed node makes the replayed nodes to be concentrated around the center of each class, incurring a potential risk of overfitting to nodes residing in those regions, which aggravates catastrophic forgetting. Moreover, as the rehearsal-based approach heavily relies on a few replayed nodes to retain knowledge obtained from previous tasks, involving the replayed nodes that have irrelevant neighbors in the model training may have a significant detrimental impact on model performance. In this paper, we propose a GCL model named DSLR, specifically, we devise a coverage-based diversity (CD) approach to consider both the class representativeness and the diversity within each class of the replayed nodes. Moreover, we adopt graph structure learning (GSL) to ensure that the replayed nodes are connected to truly informative neighbors. Extensive experimental results demonstrate the effectiveness and efficiency of DSLR. Our source code is available at https://github.com/seungyoon-Choi/DSLR_official.

Policy gradient methods are a vital ingredient behind the success of modern reinforcement learning. Modern policy gradient methods, although successful, introduce a residual error in gradient estimation. In this work, we argue that this residual term is significant and correcting for it could potentially improve sample-complexity of reinforcement learning methods. To that end, we propose log density gradient to estimate the policy gradient, which corrects for this residual error term. Log density gradient method computes policy gradient by utilising the state-action discounted distributional formulation. We first present the equations needed to exactly find the log density gradient for a tabular Markov Decision Processes (MDPs). For more complex environments, we propose a temporal difference (TD) method that approximates log density gradient by utilizing backward on-policy samples. Since backward sampling from a Markov chain is highly restrictive we also propose a min-max optimization that can approximate log density gradient using just on-policy samples. We also prove uniqueness, and convergence under linear function approximation, for this min-max optimization. Finally, we show that the sample complexity of our min-max optimization to be of the order of $m^{-1/2}$, where $m$ is the number of on-policy samples. We also demonstrate a proof-of-concept for our log density gradient method on gridworld environment, and observe that our method is able to improve upon the classical policy gradient method by a clear margin, thus indicating a promising novel direction to develop reinforcement learning algorithms that require fewer samples.