In multi-task reinforcement learning (MTRL), the objective is to simultaneously learn multiple tasks and exploit their similarity to improve the performance w.r.t.\ single-task learning. In this paper we investigate the case when all the tasks can be accurately represented in a linear approximation space using the same small subset of the original (large) set of features. This is equivalent to assuming that the weight vectors of the task value functions are \textit{jointly sparse}, i.e., the set of their non-zero components is small and it is shared across tasks. Building on existing results in multi-task regression, we develop two multi-task extensions of the fitted $Q$-iteration algorithm. While the first algorithm assumes that the tasks are jointly sparse in the given representation, the second one learns a transformation of the features in the attempt of finding a more sparse representation. For both algorithms we provide a sample complexity analysis and numerical simulations.

In Reinforcement Learning (RL), state-of-the-art algorithms require a large number of samples per state-action pair to estimate the transition kernel $p$. In many problems, a good approximation of $p$ is not needed. For instance, if from one state-action pair $(s,a)$, one can only transit to states with the same value, learning $p(\cdot|s,a)$ accurately is irrelevant (only its support matters). This paper aims at capturing such behavior by defining a novel hardness measure for Markov Decision Processes (MDPs) we call the {\em distribution-norm}. The distribution-norm w.r.t.~a measure $\nu$ is defined on zero $\nu$-mean functions $f$ by the standard variation of $f$ with respect to $\nu$. We first provide a concentration inequality for the dual of the distribution-norm. This allows us to replace the generic but loose $||\cdot||_1$ concentration inequalities used in most previous analysis of RL algorithms, to benefit from this new hardness measure. We then show that several common RL benchmarks have low hardness when measured using the new norm. The distribution-norm captures finer properties than the number of states or the diameter and can be used to assess the difficulty of MDPs.

Hippocampal place fields have been shown to reflect behaviorally relevant aspects of space. For instance, place fields tend to be skewed along commonly traveled directions, they cluster around rewarded locations, and they are constrained by the geometric structure of the environment. We hypothesize a set of design principles for the hippocampal cognitive map that explain how place fields represent space in a way that facilitates navigation and reinforcement learning. In particular, we suggest that place fields encode not just information about the current location, but also predictions about future locations under the current transition distribution. Under this model, a variety of place field phenomena arise naturally from the structure of rewards, barriers, and directional biases as reflected in the transition policy. Furthermore, we demonstrate that this representation of space can support efficient reinforcement learning. We also propose that grid cells compute the eigendecomposition of place fields in part because is useful for segmenting an enclosure along natural boundaries. When applied recursively, this segmentation can be used to discover a hierarchical decomposition of space. Thus, grid cells might be involved in computing subgoals for hierarchical reinforcement learning.

Large Markov Decision Processes (MDPs) are usually solved using Approximate Dynamic Programming (ADP) methods such as Approximate Value Iteration (AVI) or Approximate Policy Iteration (API). The main contribution of this paper is to show that, alternatively, the optimal state-action value function can be estimated using Difference of Convex functions (DC) Programming. To do so, we study the minimization of a norm of the Optimal Bellman Residual (OBR) $T^*Q-Q$, where $T^*$ is the so-called optimal Bellman operator. Controlling this residual allows controlling the distance to the optimal action-value function, and we show that minimizing an empirical norm of the OBR is consistant in the Vapnik sense.

Any reinforcement learning algorithm that applies to all Markov decision processes (MDPs) will suffer $\Omega(\sqrt{SAT})$ regret on some MDP, where $T$ is the elapsed time and $S$ and $A$ are the cardinalities of the state and action spaces. This implies $T = \Omega(SA)$ time to guarantee a near-optimal policy. In many settings of practical interest, due to the curse of dimensionality, $S$ and $A$ can be so enormous that this learning time is unacceptable. We establish that, if the system is known to be a \emph{factored} MDP, it is possible to achieve regret that scales polynomially in the number of \emph{parameters} encoding the factored MDP, which may be exponentially smaller than $S$ or $A$. We provide two algorithms that satisfy near-optimal regret bounds in this context: posterior sampling reinforcement learning (PSRL) and an upper confidence bound algorithm (UCRL-Factored).

The theory of discrete-time reinforcement learning (RL) has advanced rapidly over the past decades. Although primarily designed for discrete environments, many real-world RL applications are inherently continuous and complex. A major challenge in extending discrete-time algorithms to continuous-time settings is their sensitivity to time discretization, often leading to poor stability and slow convergence. In this paper, we investigate deterministic policy gradient methods for continuous-time RL. We derive a continuous-time policy gradient formula based on an analogue of the advantage function and establish its martingale characterization. This theoretical foundation leads to our proposed algorithm, CT-DDPG, which enables stable learning with deterministic policies in continuous-time environments. Numerical experiments show that the proposed CT-DDPG algorithm offers improved stability and faster convergence compared to existing discrete-time and continuous-time methods, across a wide range of control tasks with varying time discretizations and noise levels.

Abstract--Dynamic V oltage and Frequency Scaling (DVFS) is essential for enhancing energy efficiency in mobile platforms. However, traditional heuristic-based governors are increasingly inadequate for managing the complexity of heterogeneous System-on-Chip designs and diverse application workloads. Although reinforcement learning approaches offer improved performance, their poor generalization capability and reliance on extensive retraining for each hardware and application combination leads to significant deployment costs. In this work, we observe that device and application metadata inherently encapsulate valuable knowledge for DVFS, presenting an opportunity to overcome these limitations. We formulate DVFS for heterogeneous devices and applications as a multi-task reinforcement learning problem. We introduce MetaDVFS, which is a metadata-guided framework that systematically leverages metadata to discover and transfer shared knowledge across DVFS tasks. Evaluations on five Google Pixel devices running six applications show that MetaDVFS achieves up to 17% improvement in Performance-Power Ratio and up to 26% improvement in Quality of Experience. Compared to state-of-the-art methods, MetaDVFS delivers 70.8% faster adaptation (3.5 1.1 vs. 11.8 5.2 minutes) and 5.8-27.6% These results establish MetaDVFS as an effective and scalable solution for DVFS deployment in heterogeneous mobile environments. Dynamic V oltage and Frequency Scaling (DVFS) is an essential technique for effectively improving energy efficiency in battery-powered mobile platforms. DVFS adjusts the operating voltage and frequency of a device in response to current workload demands [1]. Experimental evaluations report energy savings exceeding 26% on mobile MPSoCs where DVFS functions compared to statically managed systems [2]. Traditional DVFS policies typically rely on heuristic-based governors, such as ondemand and schedutil, which make frequency decisions based primarily on simple utilization metrics. Jinqi Y an, Qianlong Sang, Yili Gong, Chuang Hu, and Dazhao Cheng are with the School of Computer Science, Wuhan University.

Recent reinforcement learning (RL) methods have substantially enhanced the planning capabilities of Large Language Models (LLMs), yet the theoretical basis for their effectiveness remains elusive. In this work, we investigate RL's benefits and limitations through a tractable graph-based abstraction, focusing on policy gradient (PG) and Q-learning methods. Our theoretical analyses reveal that supervised fine-tuning (SFT) may introduce co-occurrence-based spurious solutions, whereas RL achieves correct planning primarily through exploration, underscoring exploration's role in enabling better generalization. However, we also show that PG suffers from diversity collapse, where output diversity decreases during training and persists even after perfect accuracy is attained. By contrast, Q-learning provides two key advantages: off-policy learning and diversity preservation at convergence. We further demonstrate that careful reward design is necessary to prevent reward hacking in Q-learning. Finally, applying our framework to the real-world planning benchmark Blocksworld, we confirm that these behaviors manifest in practice. Planning is a fundamental cognitive construct that underpins human intelligence, shaping our ability to organize tasks, coordinate activities, and formulate complex solutions such as mathematical proofs. It enables humans to decompose complex goals into manageable steps, anticipate potential challenges, and maintain coherence during problem solving. Similarly, planning plays a pivotal role in state-of-the-art Large Language Models (LLMs), enhancing their ability to address structured and long-horizon tasks with greater accuracy and reliability. Early generations of LLMs primarily relied on next-token prediction and passive statistical learning, which limited their planning capabilities to short-horizon, reactive responses.

Smart contract-based automation of financial derivatives offers substantial efficiency gains, but its real-world adoption is constrained by the complexity of translating financial specifications into gas-efficient executable code. In particular, generating code that is both functionally correct and economically viable from high-level specifications, such as the Common Domain Model (CDM), remains a significant challenge. This paper introduces a Reinforcement Learning (RL) framework to generate functional and gas-optimized Solidity smart contracts directly from CDM specifications. We employ a Proximal Policy Optimization (PPO) agent that learns to select optimal code snippets from a pre-defined library. To manage the complex search space, a two-phase curriculum first trains the agent for functional correctness before shifting its focus to gas optimization. Our empirical results show the RL agent learns to generate contracts with significant gas savings, achieving cost reductions of up to 35.59% on unseen test data compared to unoptimized baselines. This work presents a viable methodology for the automated synthesis of reliable and economically sustainable smart contracts, bridging the gap between high-level financial agreements and efficient on-chain execution.

Sample efficiency is a central property of effective deep reinforcement learning algorithms. Recent work has improved this through added complexity, such as larger models, exotic network architectures, and more complex algorithms, which are typically motivated purely by empirical performance. We take a more principled approach by focusing on the optimization landscape of the critic network. Using the eigenspectrum and condition number of the critic's Hessian, we systematically investigate the impact of common architectural design decisions on training dynamics. Our analysis reveals that a novel combination of batch normalization (BN), weight normalization (WN), and a distributional cross-entropy (CE) loss produces condition numbers orders of magnitude smaller than baselines. This combination also naturally bounds gradient norms, a property critical for maintaining a stable effective learning rate under non-stationary targets and bootstrapping. Based on these insights, we introduce XQC: a well-motivated, sample-efficient deep actor-critic algorithm built upon soft actor-critic that embodies these optimization-aware principles. We achieve state-of-the-art sample efficiency across 55 proprioception and 15 vision-based continuous control tasks, all while using significantly fewer parameters than competing methods.