Online Market Making and the Value of Observing the Order Book

We study an online market-making problem in which a learner sequentially posts bid and ask prices for a single asset while interacting with traders holding private valuations. Unlike existing online learning formulations that assume fully censored feedback, we introduce an action-dependent feedback model inspired by real limit order books: when a trade occurs, the trader's valuation remains hidden, whereas when no trade occurs, informative feedback about supply and demand is revealed. We show that this additional information fundamentally changes the learnability of the problem. In the stochastic setting with i.i.d. market prices, we propose an elimination-based algorithm that achieves $O(\sqrt T)$ regret with high probability, without requiring any smoothness assumptions on the distribution of trader valuations. We then extend this result to a broad class of mean-reverting price processes by considering both local, autoregressive dynamics and a weaker global drift condition based on cumulative deviations from the mean. Under either assumption, we establish high-probability $O(\sqrt T)$ regret bounds, relying on a new concentration inequality of independent interest. Finally, in the adversarial setting with oblivious prices, we design an explore-then-perturb algorithm that guarantees $O(T^{2/3})$ regret in expectation. Our results quantify the value of observing the order book in online market making and demonstrate that even limited, action-dependent feedback can substantially improve regret guarantees compared to standard bandit feedback models.

Unsupervised Behavioral Compression: Learning Low-Dimensional Policy Manifolds through State-Occupancy Matching

Deep Reinforcement Learning (DRL) is widely recognized as sample-inefficient, a limitation attributable in part to the high dimensionality and substantial functional redundancy inherent to the policy parameter space. A recent framework, which we refer to as Action-based Policy Compression (APC), mitigates this issue by compressing the parameter space $Θ$ into a low-dimensional latent manifold $\mathcal Z$ using a learned generative mapping $g:\mathcal Z \to Θ$. However, its performance is severely constrained by relying on immediate action-matching as a reconstruction loss, a myopic proxy for behavioral similarity that suffers from compounding errors across sequential decisions. To overcome this bottleneck, we introduce Occupancy-based Policy Compression (OPC), which enhances APC by shifting behavior representation from immediate action-matching to long-horizon state-space coverage. Specifically, we propose two principal improvements: (1) we curate the dataset generation with an information-theoretic uniqueness metric that delivers a diverse population of policies; and (2) we propose a fully differentiable compression objective that directly minimizes the divergence between the true and reconstructed mixture occupancy distributions. These modifications force the generative model to organize the latent space around true functional similarity, promoting a latent representation that generalizes over a broad spectrum of behaviors while retaining most of the original parameter space's expressivity. Finally, we empirically validate the advantages of our contributions across multiple continuous control benchmarks.

How Log-Barrier Helps Exploration in Policy Optimization

Recently, it has been shown that the Stochastic Gradient Bandit (SGB) algorithm converges to a globally optimal policy with a constant learning rate. However, these guarantees rely on unrealistic assumptions about the learning process, namely that the probability of the optimal action is always bounded away from zero. We attribute this to the lack of an explicit exploration mechanism in SGB. To address these limitations, we propose to regularize the SGB objective with a log-barrier on the parametric policy, structurally enforcing a minimal amount of exploration. We prove that Log-Barrier Stochastic Gradient Bandit (LB-SGB) matches the sample complexity of SGB, but also converges (at a slower rate) without any assumptions on the learning process. We also show a connection between the log-barrier regularization and Natural Policy Gradient, as both exploit the geometry of the policy space by controlling the Fisher information. We validate our theoretical findings through numerical simulations, showing the benefits of the log-barrier regularization.

Learning in Markov Decision Processes with Exogenous Dynamics

Reinforcement learning algorithms are typically designed for generic Markov Decision Processes (MDPs), where any state-action pair can lead to an arbitrary transition distribution. In many practical systems, however, only a subset of the state variables is directly influenced by the agent's actions, while the remaining components evolve according to exogenous dynamics and account for most of the stochasticity. In this work, we study a structured class of MDPs characterized by exogenous state components whose transitions are independent of the agent's actions. We show that exploiting this structure yields significantly improved learning guarantees, with only the size of the exogenous state space appearing in the leading terms of the regret bounds. We further establish a matching lower bound, showing that this dependence is information-theoretically optimal. Finally, we empirically validate our approach across classical toy settings and real-world-inspired environments, demonstrating substantial gains in sample efficiency compared to standard reinforcement learning methods.

K-Myriad: Jump-starting reinforcement learning with unsupervised parallel agents

Parallelization in Reinforcement Learning is typically employed to speed up the training of a single policy, where multiple workers collect experience from an identical sampling distribution. This common design limits the potential of parallelization by neglecting the advantages of diverse exploration strategies. We propose K-Myriad, a scalable and unsupervised method that maximizes the collective state entropy induced by a population of parallel policies. By cultivating a portfolio of specialized exploration strategies, K-Myriad provides a robust initialization for Reinforcement Learning, leading to both higher training efficiency and the discovery of heterogeneous solutions. Experiments on high-dimensional continuous control tasks, with large-scale parallelization, demonstrate that K-Myriad can learn a broad set of distinct policies, highlighting its effectiveness for collective exploration and paving the way towards novel parallelization strategies.

From Parameters to Behavior: Unsupervised Compression of the Policy Space

Despite its recent successes, Deep Reinforcement Learning (DRL) is notoriously sample-inefficient. We argue that this inefficiency stems from the standard practice of optimizing policies directly in the high-dimensional and highly redundant parameter space $\Theta$. This challenge is greatly compounded in multi-task settings. In this work, we develop a novel, unsupervised approach that compresses the policy parameter space $\Theta$ into a low-dimensional latent space $\mathcal{Z}$. We train a generative model $g:\mathcal{Z}\to\Theta$ by optimizing a behavioral reconstruction loss, which ensures that the latent space is organized by functional similarity rather than proximity in parameterization. We conjecture that the inherent dimensionality of this manifold is a function of the environment's complexity, rather than the size of the policy network. We validate our approach in continuous control domains, showing that the parameterization of standard policy networks can be compressed up to five orders of magnitude while retaining most of its expressivity. As a byproduct, we show that the learned manifold enables task-specific adaptation via Policy Gradient operating in the latent space $\mathcal{Z}$.

Limitations of Physics-Informed Neural Networks: a Study on Smart Grid Surrogation

Physics-Informed Neural Networks (PINNs) present a transformative approach for smart grid modeling by integrating physical laws directly into learning frameworks, addressing critical challenges of data scarcity and physical consistency in conventional data-driven methods. This paper evaluates PINNs' capabilities as surrogate models for smart grid dynamics, comparing their performance against XGBoost, Random Forest, and Linear Regression across three key experiments: interpolation, cross-validation, and episodic trajectory prediction. By training PINNs exclusively through physics-based loss functions (enforcing power balance, operational constraints, and grid stability) we demonstrate their superior generalization, outperforming data-driven models in error reduction. Notably, PINNs maintain comparatively lower MAE in dynamic grid operations, reliably capturing state transitions in both random and expert-driven control scenarios, while traditional models exhibit erratic performance. Despite slight degradation in extreme operational regimes, PINNs consistently enforce physical feasibility, proving vital for safety-critical applications. Our results contribute to establishing PINNs as a paradigm-shifting tool for smart grid surrogation, bridging data-driven flexibility with first-principles rigor. This work advances real-time grid control and scalable digital twins, emphasizing the necessity of physics-aware architectures in mission-critical energy systems.

"So, Tell Me About Your Policy...": Distillation of interpretable policies from Deep Reinforcement Learning agents

Recent advances in Reinforcement Learning (RL) largely benefit from the inclusion of Deep Neural Networks, boosting the number of novel approaches proposed in the field of Deep Reinforcement Learning (DRL). These techniques demonstrate the ability to tackle complex games such as Atari, Go, and other real-world applications, including financial trading. Nevertheless, a significant challenge emerges from the lack of interpretability, particularly when attempting to comprehend the underlying patterns learned, the relative importance of the state features, and how they are integrated to generate the policy's output. For this reason, in mission-critical and real-world settings, it is often preferred to deploy a simpler and more interpretable algorithm, although at the cost of performance. In this paper, we propose a novel algorithm, supported by theoretical guarantees, that can extract an interpretable policy (e.g., a linear policy) without disregarding the peculiarities of expert behavior. This result is obtained by considering the advantage function, which includes information about why an action is superior to the others. In contrast to previous works, our approach enables the training of an interpretable policy using previously collected experience. The proposed algorithm is empirically evaluated on classic control environments and on a financial trading scenario, demonstrating its ability to extract meaningful information from complex expert policies.

Enhancing Diversity in Parallel Agents: A Maximum State Entropy Exploration Story

Parallel data collection has redefined Reinforcement Learning (RL), unlocking unprecedented efficiency and powering breakthroughs in large-scale real-world applications. In this paradigm, $N$ identical agents operate in $N$ replicas of an environment simulator, accelerating data collection by a factor of $N$. A critical question arises: \textit{Does specializing the policies of the parallel agents hold the key to surpass the $N$ factor acceleration?} In this paper, we introduce a novel learning framework that maximizes the entropy of collected data in a parallel setting. Our approach carefully balances the entropy of individual agents with inter-agent diversity, effectively minimizing redundancies. The latter idea is implemented with a centralized policy gradient method, which shows promise when evaluated empirically against systems of identical agents, as well as synergy with batch RL techniques that can exploit data diversity. Finally, we provide an original concentration analysis that shows faster rates for specialized parallel sampling distributions, which supports our methodology and may be of independent interest.

Towards Principled Multi-Agent Task Agnostic Exploration

In reinforcement learning, we typically refer to task-agnostic exploration when we aim to explore the environment without access to the task specification a priori. In a single-agent setting the problem has been extensively studied and mostly understood. A popular approach cast the task-agnostic objective as maximizing the entropy of the state distribution induced by the agent's policy, from which principles and methods follows. In contrast, little is known about task-agnostic exploration in multi-agent settings, which are ubiquitous in the real world. How should different agents explore in the presence of others? In this paper, we address this question through a generalization to multiple agents of the problem of maximizing the state distribution entropy. First, we investigate alternative formulations, highlighting respective positives and negatives. Then, we present a scalable, decentralized, trust-region policy search algorithm to address the problem in practical settings. Finally, we provide proof of concept experiments to both corroborate the theoretical findings and pave the way for task-agnostic exploration in challenging multi-agent settings.