We present a bound for value-prediction error with respect to model misspecification that is tight, including constant factors. This is a direct improvement of the "simulation lemma," a foundational result in reinforcement learning. We demonstrate that existing bounds are quite loose, becoming vacuous for large discount factors, due to the suboptimal treatment of compounding probability errors. By carefully considering this quantity on its own, instead of as a subcomponent of value error, we derive a bound that is sub-linear with respect to transition function misspecification. We then demonstrate broader applicability of this technique, improving a similar bound in the related subfield of hierarchical abstraction.

Diffusion-based models have achieved notable empirical successes in reinforcement learning (RL) due to their expressiveness in modeling complex distributions. Despite existing methods being promising, the key challenge of extending existing methods for broader real-world applications lies in the computational cost at inference time, i.e., sampling from a diffusion model is considerably slow as it often requires tens to hundreds of iterations to generate even one sample. To circumvent this issue, we propose to leverage the flexibility of diffusion models for RL from a representation learning perspective. In particular, by exploiting the connection between diffusion model and energy-based model, we develop Diffusion Spectral Representation (Diff-SR), a coherent algorithm framework that enables extracting sufficient representations for value functions in Markov decision processes (MDP) and partially observable Markov decision processes (POMDP). We further demonstrate how Diff-SR facilitates efficient policy optimization and practical algorithms while explicitly bypassing the difficulty and inference cost of sampling from the diffusion model. Finally, we provide comprehensive empirical studies to verify the benefits of Diff-SR in delivering robust and advantageous performance across various benchmarks with both fully and partially observable settings.

We consider a variant of the stochastic gradient descent (SGD) with a random learning rate and reveal its convergence properties. SGD is a widely used stochastic optimization algorithm in machine learning, especially deep learning. Numerous studies reveal the convergence properties of SGD and its simplified variants. Among these, the analysis of convergence using a stationary distribution of updated parameters provides generalizable results. However, to obtain a stationary distribution, the update direction of the parameters must not degenerate, which limits the applicable variants of SGD. In this study, we consider a novel SGD variant, Poisson SGD, which has degenerated parameter update directions and instead utilizes a random learning rate. Consequently, we demonstrate that a distribution of a parameter updated by Poisson SGD converges to a stationary distribution under weak assumptions on a loss function. Based on this, we further show that Poisson SGD finds global minima in non-convex optimization problems and also evaluate the generalization error using this method. As a proof technique, we approximate the distribution by Poisson SGD with that of the bouncy particle sampler (BPS) and derive its stationary distribution, using the theoretical advance of the piece-wise deterministic Markov process (PDMP).

Learning a world model for model-free Reinforcement Learning (RL) agents can significantly improve the sample efficiency by learning policies in imagination. However, building a world model for Multi-Agent RL (MARL) can be particularly challenging due to the scalability issue in a centralized architecture arising from a large number of agents, and also the non-stationarity issue in a decentralized architecture stemming from the inter-dependency among agents. To address both challenges, we propose a novel world model for MARL that learns decentralized local dynamics for scalability, combined with a centralized representation aggregation from all agents. We cast the dynamics learning as an auto-regressive sequence modeling problem over discrete tokens by leveraging the expressive Transformer architecture, in order to model complex local dynamics across different agents and provide accurate and consistent long-term imaginations. As the first pioneering Transformer-based world model for multi-agent systems, we introduce a Perceiver Transformer as an effective solution to enable centralized representation aggregation within this context. Results on Starcraft Multi-Agent Challenge (SMAC) show that it outperforms strong model-free approaches and existing model-based methods in both sample efficiency and overall performance.

Statistical model discovery is a challenging search over a vast space of models subject to domain-specific constraints. Efficiently searching over this space requires expertise in modeling and the problem domain. Motivated by the domain knowledge and programming capabilities of large language models (LMs), we introduce a method for language model driven automated statistical model discovery. We cast our automated procedure within the principled framework of Box's Loop: the LM iterates between proposing statistical models represented as probabilistic programs, acting as a modeler, and critiquing those models, acting as a domain expert. By leveraging LMs, we do not have to define a domain-specific language of models or design a handcrafted search procedure, which are key restrictions of previous systems. We evaluate our method in three settings in probabilistic modeling: searching within a restricted space of models, searching over an open-ended space, and improving expert models under natural language constraints (e.g., this model should be interpretable to an ecologist). Our method identifies models on par with human expert designed models and extends classic models in interpretable ways. Our results highlight the promise of LM-driven model discovery.

Hierarchical Reinforcement Learning (HRL) approaches have shown successful results in solving a large variety of complex, structured, long-horizon problems. Nevertheless, a full theoretical understanding of this empirical evidence is currently missing. In the context of the \emph{option} framework, prior research has devised efficient algorithms for scenarios where options are fixed, and the high-level policy selecting among options only has to be learned. However, the fully realistic scenario in which both the high-level and the low-level policies are learned is surprisingly disregarded from a theoretical perspective. This work makes a step towards the understanding of this latter scenario. Focusing on the finite-horizon problem, we present a meta-algorithm alternating between regret minimization algorithms instanced at different (high and low) temporal abstractions. At the higher level, we treat the problem as a Semi-Markov Decision Process (SMDP), with fixed low-level policies, while at a lower level, inner option policies are learned with a fixed high-level policy. The bounds derived are compared with the lower bound for non-hierarchical finite-horizon problems, allowing to characterize when a hierarchical approach is provably preferable, even without pre-trained options.

Reinforcement Learning (RL) has shown great empirical success in various application domains. The theoretical aspects of the problem have been extensively studied over past decades, particularly under tabular and linear Markov Decision Process structures. Recently, non-linear function approximation using kernel-based prediction has gained traction. This approach is particularly interesting as it naturally extends the linear structure, and helps explain the behavior of neural-network-based models at their infinite width limit. The analytical results however do not adequately address the performance guarantees for this case. We will highlight this open problem, overview existing partial results, and discuss related challenges.

This paper presents a novel approach to address the challenging problem of autonomous on-ramp merging, where a self-driving vehicle needs to seamlessly integrate into a flow of vehicles on a multi-lane highway. We introduce the Lane-keeping, Lane-changing with Latent-state Inference and Safety Controller (L3IS) agent, designed to perform the on-ramp merging task safely without comprehensive knowledge about surrounding vehicles' intents or driving styles. We also present an augmentation of this agent called AL3IS that accounts for observation delays, allowing the agent to make more robust decisions in real-world environments with vehicle-to-vehicle (V2V) communication delays. By modeling the unobservable aspects of the environment through latent states, such as other drivers' intents, our approach enhances the agent's ability to adapt to dynamic traffic conditions, optimize merging maneuvers, and ensure safe interactions with other vehicles. We demonstrate the effectiveness of our method through extensive simulations generated from real traffic data and compare its performance with existing approaches. L3IS shows a 99.90% success rate in a challenging on-ramp merging case generated from the real US Highway 101 data. We further perform a sensitivity analysis on AL3IS to evaluate its robustness against varying observation delays, which demonstrates an acceptable performance of 93.84% success rate in 1-second V2V communication delay.

We study the question: How can we select the right data for fine-tuning to a specific task? We call this data selection problem active fine-tuning and show that it is an instance of transductive active learning, a novel generalization of classical active learning. We propose ITL, short for information-based transductive learning, an approach which samples adaptively to maximize information gained about the specified task. We are the first to show, under general regularity assumptions, that such decision rules converge uniformly to the smallest possible uncertainty obtainable from the accessible data. We apply ITL to the few-shot fine-tuning of large neural networks and show that fine-tuning with ITL learns the task with significantly fewer examples than the state-of-the-art.

Deep reinforcement learning has shown promise in various engineering applications, including vehicular traffic control. The non-stationary nature of traffic, especially in the lane-free environment with more degrees of freedom in vehicle behaviors, poses challenges for decision-making since a wrong action might lead to a catastrophic failure. In this paper, we propose a novel driving strategy for Connected and Automated Vehicles (CAVs) based on a competitive Multi-Agent Deep Deterministic Policy Gradient approach. The developed multi-agent deep reinforcement learning algorithm creates a dynamic and non-stationary scenario, mirroring real-world traffic complexities and making trained agents more robust. The algorithm's reward function is strategically and uniquely formulated to cover multiple vehicle control tasks, including maintaining desired speeds, overtaking, collision avoidance, and merging and diverging maneuvers. Moreover, additional considerations for both lateral and longitudinal passenger comfort and safety criteria are taken into account. We employed inter-vehicle forces, known as nudging and repulsive forces, to manage the maneuvers of CAVs in a lane-free traffic environment. The proposed driving algorithm is trained and evaluated on lane-free roads using the Simulation of Urban Mobility platform. Experimental results demonstrate the algorithm's efficacy in handling different objectives, highlighting its potential to enhance safety and efficiency in autonomous driving within lane-free traffic environments.