Giovanni Montana

Alex Beeson, Giovanni Montana

The ability to discover optimal behaviour from fixed data sets has the potential to transfer the successes of reinforcement learning (RL) to domains where data collection is acutely problematic. In this offline setting, a key challenge is overcoming overestimation bias for actions not present in data which, without the ability to correct for via interaction with the environment, can propagate and compound during training, leading to highly sub-optimal policies. One simple method to reduce this bias is to introduce a policy constraint via behavioural cloning (BC), which encourages agents to pick actions closer to the source data. By finding the right balance between RL and BC such approaches have been shown to be surprisingly effective while requiring minimal changes to the underlying algorithms they are based on. To date this balance has been held constant, but in this work we explore the idea of tipping this balance towards RL following initial training. Using TD3-BC, we demonstrate that by continuing to train a policy offline while reducing the influence of the BC component we can produce refined policies that outperform the original baseline, as well as match or exceed the performance of more complex alternatives. Furthermore, we demonstrate such an approach can be used for stable online fine-tuning, allowing policies to be safely improved during deployment.

David Ireland, Giovanni Montana

Combinatorial Optimisation problems arise in several application domains and are often formulated in terms of graphs. Many of these problems are NP-hard, but exact solutions are not always needed. Several heuristics have been developed to provide near-optimal solutions; however, they do not typically scale well with the size of the graph. We propose a low-complexity approach for identifying a (possibly much smaller) subgraph of the original graph where the heuristics can be run in reasonable time and with a high likelihood of finding a global near-optimal solution. The core component of our approach is LeNSE, a reinforcement learning algorithm that learns how to navigate the space of possible subgraphs using an Euclidean subgraph embedding as its map. To solve CO problems, LeNSE is provided with a discriminative embedding trained using any existing heuristics using only on a small portion of the original graph. When tested on three problems (vertex cover, max-cut and influence maximisation) using real graphs with up to $10$ million edges, LeNSE identifies small subgraphs yielding solutions comparable to those found by running the heuristics on the entire graph, but at a fraction of the total run time.

Alex Beeson, Giovanni Montana

Offline reinforcement learning agents seek optimal policies from fixed data sets. With environmental interaction prohibited, agents face significant challenges in preventing errors in value estimates from compounding and subsequently causing the learning process to collapse. Uncertainty estimation using ensembles compensates for this by penalising high-variance value estimates, allowing agents to learn robust policies based on data-driven actions. However, the requirement for large ensembles to facilitate sufficient penalisation results in significant computational overhead. In this work, we examine the role of policy constraints as a mechanism for regulating uncertainty, and the corresponding balance between level of constraint and ensemble size. By incorporating behavioural cloning into policy updates, we show empirically that sufficient penalisation can be achieved with a much smaller ensemble size, substantially reducing computational demand while retaining state-of-the-art performance on benchmarking tasks. Furthermore, we show how such an approach can facilitate stable online fine tuning, allowing for continued policy improvement while avoiding severe performance drops.

Charles A. Hepburn, Giovanni Montana

In many real-world applications, collecting large and high-quality datasets may be too costly or impractical. Offline reinforcement learning (RL) aims to infer an optimal decision-making policy from a fixed set of data. Getting the most information from historical data is then vital for good performance once the policy is deployed. We propose a model-based data augmentation strategy, Trajectory Stitching (TS), to improve the quality of sub-optimal historical trajectories. TS introduces unseen actions joining previously disconnected states: using a probabilistic notion of state reachability, it effectively `stitches' together parts of the historical demonstrations to generate new, higher quality ones. A stitching event consists of a transition between a pair of observed states through a synthetic and highly probable action. New actions are introduced only when they are expected to be beneficial, according to an estimated state-value function. We show that using this data augmentation strategy jointly with behavioural cloning (BC) leads to improvements over the behaviour-cloned policy from the original dataset. Improving over the BC policy could then be used as a launchpad for online RL through planning and demonstration-guided RL.

Charles A. Hepburn, Giovanni Montana

Behavioural cloning (BC) is a commonly used imitation learning method to infer a sequential decision-making policy from expert demonstrations. However, when the quality of the data is not optimal, the resulting behavioural policy also performs sub-optimally once deployed. Recently, there has been a surge in offline reinforcement learning methods that hold the promise to extract high-quality policies from sub-optimal historical data. A common approach is to perform regularisation during training, encouraging updates during policy evaluation and/or policy improvement to stay close to the underlying data. In this work, we investigate whether an offline approach to improving the quality of the existing data can lead to improved behavioural policies without any changes in the BC algorithm. The proposed data improvement approach - Trajectory Stitching (TS) - generates new trajectories (sequences of states and actions) by `stitching' pairs of states that were disconnected in the original data and generating their connecting new action. By construction, these new transitions are guaranteed to be highly plausible according to probabilistic models of the environment, and to improve a state-value function. We demonstrate that the iterative process of replacing old trajectories with new ones incrementally improves the underlying behavioural policy. Extensive experimental results show that significant performance gains can be achieved using TS over BC policies extracted from the original data. Furthermore, using the D4RL benchmarking suite, we demonstrate that state-of-the-art results are obtained by combining TS with two existing offline learning methodologies reliant on BC, model-based offline planning (MBOP) and policy constraint (TD3+BC).

Matthew MacPherson, Keerthini Muthuswamy, Ashik Amlani et al.

Understanding the internal physiological changes accompanying the aging process is an important aspect of medical image interpretation, with the expected changes acting as a baseline when reporting abnormal findings. Deep learning has recently been demonstrated to allow the accurate estimation of patient age from chest X-rays, and shows potential as a health indicator and mortality predictor. In this paper we present a novel comparative study of the relative performance of radiologists versus state-of-the-art deep learning models on two tasks: (a) patient age estimation from a single chest X-ray, and (b) ranking of two time-separated images of the same patient by age. We train our models with a heterogeneous database of 1.8M chest X-rays with ground truth patient ages and investigate the limitations on model accuracy imposed by limited training data and image resolution, and demonstrate generalisation performance on public data. To explore the large performance gap between the models and humans on these age-prediction tasks compared with other radiological reporting tasks seen in the literature, we incorporate our age prediction model into a conditional Generative Adversarial Network (cGAN) allowing visualisation of the semantic features identified by the prediction model as significant to age prediction, comparing the identified features with those relied on by clinicians.

George Watkins, Giovanni Montana, Juergen Branke

The graph colouring problem consists of assigning labels, or colours, to the vertices of a graph such that no two adjacent vertices share the same colour. In this work we investigate whether deep reinforcement learning can be used to discover a competitive construction heuristic for graph colouring. Our proposed approach, ReLCol, uses deep Q-learning together with a graph neural network for feature extraction, and employs a novel way of parameterising the graph that results in improved performance. Using standard benchmark graphs with varied topologies, we empirically evaluate the benefits and limitations of the heuristic learned by ReLCol relative to existing construction algorithms, and demonstrate that reinforcement learning is a promising direction for further research on the graph colouring problem.

Mianchu Wang, Yue Jin, Giovanni Montana

Offline reinforcement learning (RL) aims to infer sequential decision policies using only offline datasets. This is a particularly difficult setup, especially when learning to achieve multiple different goals or outcomes under a given scenario with only sparse rewards. For offline learning of goal-conditioned policies via supervised learning, previous work has shown that an advantage weighted log-likelihood loss guarantees monotonic policy improvement. In this work we argue that, despite its benefits, this approach is still insufficient to fully address the distribution shift and multi-modality problems. The latter is particularly severe in long-horizon tasks where finding a unique and optimal policy that goes from a state to the desired goal is challenging as there may be multiple and potentially conflicting solutions. To tackle these challenges, we propose a complementary advantage-based weighting scheme that introduces an additional source of inductive bias: given a value-based partitioning of the state space, the contribution of actions expected to lead to target regions that are easier to reach, compared to the final goal, is further increased. Empirically, we demonstrate that the proposed approach, Dual-Advantage Weighted Offline Goal-conditioned RL (DAWOG), outperforms several competing offline algorithms in commonly used benchmarks. Analytically, we offer a guarantee that the learnt policy is never worse than the underlying behaviour policy.

Mianchu Wang, Rui Yang, Xi Chen et al.

Offline Goal-Conditioned RL (GCRL) offers a feasible paradigm for learning general-purpose policies from diverse and multi-task offline datasets. Despite notable recent progress, the predominant offline GCRL methods, mainly model-free, face constraints in handling limited data and generalizing to unseen goals. In this work, we propose Goal-conditioned Offline Planning (GOPlan), a novel model-based framework that contains two key phases: (1) pretraining a prior policy capable of capturing multi-modal action distribution within the multi-goal dataset; (2) employing the reanalysis method with planning to generate imagined trajectories for funetuning policies. Specifically, we base the prior policy on an advantage-weighted conditioned generative adversarial network, which facilitates distinct mode separation, mitigating the pitfalls of out-of-distribution (OOD) actions. For further policy optimization, the reanalysis method generates high-quality imaginary data by planning with learned models for both intra-trajectory and inter-trajectory goals. With thorough experimental evaluations, we demonstrate that GOPlan achieves state-of-the-art performance on various offline multi-goal navigation and manipulation tasks. Moreover, our results highlight the superior ability of GOPlan to handle small data budgets and generalize to OOD goals.

Yijun Quan, Wentai Wu, Giovanni Montana

Foundation models are commonly deployed as frozen feature extractors with a small trainable head to adapt to private, user-generated data in federated settings. The ``right to be forgotten'' requires removing the influence of specific samples or users from the trained model on demand. Existing federated unlearning methods target general deep models and rely on approximate reconstruction or selective retraining, making exactness costly or elusive. We study this problem in a practically relevant but under-explored regime: a frozen foundation model with a ridge-regression head. The exact optimum depends on the data only through two additive sufficient statistics, which we turn into a communication protocol supporting an arbitrary stream of add and delete requests via fixed-size messages. The server maintains a head that is, in exact arithmetic, pointwise identical to centralized retraining after every request. We provide deterministic retrain-equivalence guarantees, order and partition invariance, two server-side variants, and a Bayesian certificate of zero KL divergence. Experiments on four benchmarks confirm the guarantees: both variants match centralized ridge retraining to within $10^{-9}$ relative Frobenius error and complete each request at orders-of-magnitude lower cost than federated retraining baselines.

Alex Beeson, David Ireland, Giovanni Montana

Expanding reinforcement learning (RL) to offline domains generates promising prospects, particularly in sectors where data collection poses substantial challenges or risks. Pivotal to the success of transferring RL offline is mitigating overestimation bias in value estimates for state-action pairs absent from data. Whilst numerous approaches have been proposed in recent years, these tend to focus primarily on continuous or small-scale discrete action spaces. Factorised discrete action spaces, on the other hand, have received relatively little attention, despite many real-world problems naturally having factorisable actions. In this work, we undertake a formative investigation into offline reinforcement learning in factorisable action spaces. Using value-decomposition as formulated in DecQN as a foundation, we present the case for a factorised approach and conduct an extensive empirical evaluation of several offline techniques adapted to the factorised setting. In the absence of established benchmarks, we introduce a suite of our own comprising datasets of varying quality and task complexity. Advocating for reproducible research and innovation, we make all datasets available for public use alongside our code base.

Mingqi Gao, Jinyu Yang, Jingnan Luo et al.

Referring video object segmentation (RVOS) has recently generated great popularity in computer vision due to its widespread applications. Existing RVOS setting contains elaborately trimmed videos, with text-referred objects always appearing in all frames, which however fail to fully reflect the realistic challenges of this task. This simplified setting requires RVOS methods to only predict where objects, with no need to show when the objects appear. In this work, we introduce a new setting towards in-the-wild RVOS. To this end, we collect a new benchmark dataset using Youtube Untrimmed videos for RVOS - YoURVOS, which contains 1,120 in-the-wild videos with 7 times more duration and scenes than existing datasets. Our new benchmark challenges RVOS methods to show not only where but also when objects appear in videos. To set a baseline, we propose Object-level Multimodal TransFormers (OMFormer) to tackle the challenges, which are characterized by encoding object-level multimodal interactions for efficient and global spatial-temporal localisation. We demonstrate that previous VOS methods struggle on our YoURVOS benchmark, especially with the increase of target-absent frames, while our OMFormer consistently performs well. Our YoURVOS dataset offers an imperative benchmark, which will push forward the advancement of RVOS methods for practical applications.

Yujie Zhu, Charles A. Hepburn, Matthew Thorpe et al.

In reinforcement learning with sparse rewards, demonstrations can accelerate learning, but determining when to imitate them remains challenging. We propose Smooth Policy Regularisation from Demonstrations (SPReD), a framework that addresses the fundamental question: when should an agent imitate a demonstration versus follow its own policy? SPReD uses ensemble methods to explicitly model Q-value distributions for both demonstration and policy actions, quantifying uncertainty for comparisons. We develop two complementary uncertainty-aware methods: a probabilistic approach estimating the likelihood of demonstration superiority, and an advantage-based approach scaling imitation by statistical significance. Unlike prevailing methods (e.g. Q-filter) that make binary imitation decisions, SPReD applies continuous, uncertainty-proportional regularisation weights, reducing gradient variance during training. Despite its computational simplicity, SPReD achieves remarkable gains in experiments across eight robotics tasks, outperforming existing approaches by up to a factor of 14 in complex tasks while maintaining robustness to demonstration quality and quantity. Our code is available at https://github.com/YujieZhu7/SPReD.

Yue Jin, Giovanni Montana

Offline multi-agent reinforcement learning (MARL) faces a critical challenge: the joint action space grows exponentially with the number of agents, making dataset coverage exponentially sparse and out-of-distribution (OOD) joint actions unavoidable. Partial Action Replacement (PAR) mitigates this by anchoring a subset of agents to dataset actions, but existing approach relies on enumerating multiple subset configurations at high computational cost and cannot adapt to varying states. We introduce PLCQL, a framework that formulates PAR subset selection as a contextual bandit problem and learns a state-dependent PAR policy using Proximal Policy Optimisation with an uncertainty-weighted reward. This adaptive policy dynamically determines how many agents to replace at each update step, balancing policy improvement against conservative value estimation. We prove a value-error bound showing that the estimation error scales linearly with the expected number of deviating agents. Compared with the previous PAR-based method SPaCQL, PLCQL reduces the number of per-iteration Q-function evaluations from n to 1, significantly improving computational efficiency. Empirically, PLCQL achieves the highest normalised scores on 66% of tasks across MPE, MaMuJoCo, and SMAC benchmarks, outperforming SPaCQL on 84% of tasks while substantially reducing computational cost.

Yue Jin, Giovanni Montana

Offline multi-agent reinforcement learning (MARL) is severely hampered by the challenge of evaluating out-of-distribution (OOD) joint actions. Our core finding is that when the behavior policy is factorized - a common scenario where agents act fully or partially independently during data collection - a strategy of partial action replacement (PAR) can significantly mitigate this challenge. PAR updates a single or part of agents' actions while the others remain fixed to the behavioral data, reducing distribution shift compared to full joint-action updates. Based on this insight, we develop Soft-Partial Conservative Q-Learning (SPaCQL), using PAR to mitigate OOD issue and dynamically weighting different PAR strategies based on the uncertainty of value estimation. We provide a rigorous theoretical foundation for this approach, proving that under factorized behavior policies, the induced distribution shift scales linearly with the number of deviating agents rather than exponentially with the joint-action space. This yields a provably tighter value error bound for this important class of offline MARL problems. Our theoretical results also indicate that SPaCQL adaptively addresses distribution shift using uncertainty-informed weights. Our empirical results demonstrate SPaCQL enables more effective policy learning, and manifest its remarkable superiority over baseline algorithms when the offline dataset exhibits the independence structure.

Mianchu Wang, Yue Jin, Giovanni Montana

Offline reinforcement learning (RL) seeks to learn optimal policies from static datasets without interacting with the environment. A common challenge is handling multi-modal action distributions, where multiple behaviours are represented in the data. Existing methods often assume unimodal behaviour policies, leading to suboptimal performance when this assumption is violated. We propose weighted imitation Learning on One Mode (LOM), a novel approach that focuses on learning from a single, promising mode of the behaviour policy. By using a Gaussian mixture model to identify modes and selecting the best mode based on expected returns, LOM avoids the pitfalls of averaging over conflicting actions. Theoretically, we show that LOM improves performance while maintaining simplicity in policy learning. Empirically, LOM outperforms existing methods on standard D4RL benchmarks and demonstrates its effectiveness in complex, multi-modal scenarios.

Enrique Adrian Villarrubia-Martin, Luis Rodriguez-Benitez, David Muñoz-Valero et al.

This paper addresses a critical challenge in the high-speed passenger railway industry: designing effective dynamic pricing strategies in the context of competing and cooperating operators. To address this, a multi-agent reinforcement learning (MARL) framework based on a non-zero-sum Markov game is proposed, incorporating random utility models to capture passenger decision making. Unlike prior studies in areas such as energy, airlines, and mobile networks, dynamic pricing for railway systems using deep reinforcement learning has received limited attention. A key contribution of this paper is a parametrisable and versatile reinforcement learning simulator designed to model a variety of railway network configurations and demand patterns while enabling realistic, microscopic modelling of user behaviour, called RailPricing-RL. This environment supports the proposed MARL framework, which models heterogeneous agents competing to maximise individual profits while fostering cooperative behaviour to synchronise connecting services. Experimental results validate the framework, demonstrating how user preferences affect MARL performance and how pricing policies influence passenger choices, utility, and overall system dynamics. This study provides a foundation for advancing dynamic pricing strategies in railway systems, aligning profitability with system-wide efficiency, and supporting future research on optimising pricing policies.

Mianchu Wang, Giovanni Montana

Retrosynthesis planning aims to decompose target molecules into available building blocks, forming a synthetic tree where each internal node represents an intermediate compound and each leaf ideally corresponds to a purchasable reactant. However, this tree becomes invalid if any leaf node is not a valid building block, making the planning process vulnerable to the "weakest link" in the synthetic route. Existing methods often optimise for average performance across branches, failing to account for this worst-case sensitivity. In this paper, we reframe retrosynthesis as a worst-path optimisation problem within tree-structured Markov Decision Processes (MDPs). We prove that this formulation admits a unique optimal solution and provides monotonic improvement guarantees. Building on this insight, we introduce Interactive Retrosynthesis Planning (InterRetro), a method that interacts with the tree MDP, learns a value function for worst-path outcomes, and improves its policy through self-imitation, preferentially reinforcing past decisions with high estimated advantage. Empirically, InterRetro achieves state-of-the-art results - solving 100% of targets on the Retro*-190 benchmark, shortening synthetic routes by 4.9%, and achieving promising performance using only 10% of the training data.

Yijun Quan, Zushu Li, Giovanni Montana

Growing data privacy demands, driven by regulations like GDPR and CCPA, require machine unlearning methods capable of swiftly removing the influence of specific training points. Although verified approaches like SISA, using data slicing and checkpointing, achieve efficient unlearning for single models by reverting to intermediate states, these methods struggle in teacher-student knowledge distillation settings. Unlearning in the teacher typically forces costly, complete student retraining due to pervasive information propagation during distillation. Our primary contribution is PURGE (Partitioned Unlearning with Retraining Guarantee for Ensembles), a novel framework integrating verified unlearning with distillation. We introduce constituent mapping and an incremental multi-teacher strategy that partitions the distillation process, confines each teacher constituent's impact to distinct student data subsets, and crucially maintains data isolation. The PURGE framework substantially reduces retraining overhead, requiring only partial student updates when teacher-side unlearning occurs. We provide both theoretical analysis, quantifying significant speed-ups in the unlearning process, and empirical validation on multiple datasets, demonstrating that PURGE achieves these efficiency gains while maintaining student accuracy comparable to standard baselines.

Natinael Solomon Neggatu, Jeremie Houssineau, Giovanni Montana

Offline reinforcement learning (RL) looks at learning how to optimally solve tasks using a fixed dataset of interactions from the environment. Many off-policy algorithms developed for online learning struggle in the offline setting as they tend to over-estimate the behaviour of out of distributions actions. Existing offline RL algorithms adapt off-policy algorithms, employing techniques such as constraining the policy or modifying the value function to achieve good performance on individual datasets but struggle to adapt to different tasks or datasets of different qualities without tuning hyper-parameters. We introduce a policy switching technique that dynamically combines the behaviour of a pure off-policy RL agent, for improving behaviour, and a behavioural cloning (BC) agent, for staying close to the data. We achieve this by using a combination of epistemic uncertainty, quantified by our RL model, and a metric for aleatoric uncertainty extracted from the dataset. We show empirically that our policy switching technique can outperform not only the individual algorithms used in the switching process but also compete with state-of-the-art methods on numerous benchmarks. Our use of epistemic uncertainty for policy switching also allows us to naturally extend our method to the domain of offline to online fine-tuning allowing our model to adapt quickly and safely from online data, either matching or exceeding the performance of current methods that typically require additional modification or hyper-parameter fine-tuning.

Sharlin Utke, Jeremie Houssineau, Giovanni Montana

This paper explores the impact of relational state abstraction on sample efficiency and performance in collaborative Multi-Agent Reinforcement Learning. The proposed abstraction is based on spatial relationships in environments where direct communication between agents is not allowed, leveraging the ubiquity of spatial reasoning in real-world multi-agent scenarios. We introduce MARC (Multi-Agent Relational Critic), a simple yet effective critic architecture incorporating spatial relational inductive biases by transforming the state into a spatial graph and processing it through a relational graph neural network. The performance of MARC is evaluated across six collaborative tasks, including a novel environment with heterogeneous agents. We conduct a comprehensive empirical analysis, comparing MARC against state-of-the-art MARL baselines, demonstrating improvements in both sample efficiency and asymptotic performance, as well as its potential for generalization. Our findings suggest that a minimal integration of spatial relational inductive biases as abstraction can yield substantial benefits without requiring complex designs or task-specific engineering. This work provides insights into the potential of relational state abstraction to address sample efficiency, a key challenge in MARL, offering a promising direction for developing more efficient algorithms in spatially complex environments.

Yue Jin, Shuangqing Wei, Giovanni Montana

In human society, the conflict between self-interest and collective well-being often obstructs efforts to achieve shared welfare. Related concepts like the Tragedy of the Commons and Social Dilemmas frequently manifest in our daily lives. As artificial agents increasingly serve as autonomous proxies for humans, we propose a novel multi-agent reinforcement learning (MARL) method to address this issue - learning policies to maximise collective returns even when individual agents' interests conflict with the collective one. Unlike traditional cooperative MARL solutions that involve sharing rewards, values, and policies or designing intrinsic rewards to encourage agents to learn collectively optimal policies, we propose a novel MARL approach where agents exchange action suggestions. Our method reveals less private information compared to sharing rewards, values, or policies, while enabling effective cooperation without the need to design intrinsic rewards. Our algorithm is supported by our theoretical analysis that establishes a bound on the discrepancy between collective and individual objectives, demonstrating how sharing suggestions can align agents' behaviours with the collective objective. Experimental results demonstrate that our algorithm performs competitively with baselines that rely on value or policy sharing or intrinsic rewards.

Ting Zhu, Yue Jin, Jeremie Houssineau et al.

In decentralized multi-agent reinforcement learning, agents learning in isolation can lead to relative over-generalization (RO), where optimal joint actions are undervalued in favor of suboptimal ones. This hinders effective coordination in cooperative tasks, as agents tend to choose actions that are individually rational but collectively suboptimal. To address this issue, we introduce MaxMax Q-Learning (MMQ), which employs an iterative process of sampling and evaluating potential next states, selecting those with maximal Q-values for learning. This approach refines approximations of ideal state transitions, aligning more closely with the optimal joint policy of collaborating agents. We provide theoretical analysis supporting MMQ's potential and present empirical evaluations across various environments susceptible to RO. Our results demonstrate that MMQ frequently outperforms existing baselines, exhibiting enhanced convergence and sample efficiency.

Charles A. Hepburn, Yue Jin, Giovanni Montana

Traditional offline reinforcement learning (RL) methods predominantly operate in a batch-constrained setting. This confines the algorithms to a specific state-action distribution present in the dataset, reducing the effects of distributional shift but restricting the policy to seen actions. In this paper, we alleviate this limitation by introducing state-constrained offline RL, a novel framework that focuses solely on the dataset's state distribution. This approach allows the policy to take high-quality out-of-distribution actions that lead to in-distribution states, significantly enhancing learning potential. The proposed setting not only broadens the learning horizon but also improves the ability to combine different trajectories from the dataset effectively, a desirable property inherent in offline RL. Our research is underpinned by theoretical findings that pave the way for subsequent advancements in this area. Additionally, we introduce StaCQ, a deep learning algorithm that achieves state-of-the-art performance on the D4RL benchmark datasets and aligns with our theoretical propositions. StaCQ establishes a strong baseline for forthcoming explorations in this domain.

David Ireland, Giovanni Montana

Discrete-action reinforcement learning algorithms often falter in tasks with high-dimensional discrete action spaces due to the vast number of possible actions. A recent advancement leverages value-decomposition, a concept from multi-agent reinforcement learning, to tackle this challenge. This study delves deep into the effects of this value-decomposition, revealing that whilst it curtails the over-estimation bias inherent to Q-learning algorithms, it amplifies target variance. To counteract this, we present an ensemble of critics to mitigate target variance. Moreover, we introduce a regularisation loss that helps to mitigate the effects that exploratory actions in one dimension can have on the value of optimal actions in other dimensions. Our novel algorithm, REValueD, tested on discretised versions of the DeepMind Control Suite tasks, showcases superior performance, especially in the challenging humanoid and dog tasks. We further dissect the factors influencing REValueD's performance, evaluating the significance of the regularisation loss and the scalability of REValueD with increasing sub-actions per dimension.

Nick Byrne, James R Clough, Isra Valverde et al.

Multi-class segmentation of cardiac magnetic resonance (CMR) images seeks a separation of data into anatomical components with known structure and configuration. The most popular CNN-based methods are optimised using pixel wise loss functions, ignorant of the spatially extended features that characterise anatomy. Therefore, whilst sharing a high spatial overlap with the ground truth, inferred CNN-based segmentations can lack coherence, including spurious connected components, holes and voids. Such results are implausible, violating anticipated anatomical topology. In response, (single-class) persistent homology-based loss functions have been proposed to capture global anatomical features. Our work extends these approaches to the task of multi-class segmentation. Building an enriched topological description of all class labels and class label pairs, our loss functions make predictable and statistically significant improvements in segmentation topology using a CNN-based post-processing framework. We also present (and make available) a highly efficient implementation based on cubical complexes and parallel execution, enabling practical application within high resolution 3D data for the first time. We demonstrate our approach on 2D short axis and 3D whole heart CMR segmentation, advancing a detailed and faithful analysis of performance on two publicly available datasets.

Aydan Gasimova, Giovanni Montana, Daniel Rueckert

Gathering manually annotated images for the purpose of training a predictive model is far more challenging in the medical domain than for natural images as it requires the expertise of qualified radiologists. We therefore propose to take advantage of past radiological exams (specifically, knee X-ray examinations) and formulate a framework capable of learning the correspondence between the images and reports, and hence be capable of generating diagnostic reports for a given X-ray examination consisting of an arbitrary number of image views. We demonstrate how aggregating the image features of individual exams and using them as conditional inputs when training a language generation model results in auto-generated exam reports that correlate well with radiologist-generated reports.

Henry Charlesworth, Giovanni Montana

Training agents to autonomously learn how to use anthropomorphic robotic hands has the potential to lead to systems capable of performing a multitude of complex manipulation tasks in unstructured and uncertain environments. In this work, we first introduce a suite of challenging simulated manipulation tasks that current reinforcement learning and trajectory optimisation techniques find difficult. These include environments where two simulated hands have to pass or throw objects between each other, as well as an environment where the agent must learn to spin a long pen between its fingers. We then introduce a simple trajectory optimisation that performs significantly better than existing methods on these environments. Finally, on the challenging PenSpin task we combine sub-optimal demonstrations generated through trajectory optimisation with off-policy reinforcement learning, obtaining performance that far exceeds either of these approaches individually, effectively solving the environment. Videos of all of our results are available at: https://dexterous-manipulation.github.io/

Nick Byrne, James R. Clough, Giovanni Montana et al.

With respect to spatial overlap, CNN-based segmentation of short axis cardiovascular magnetic resonance (CMR) images has achieved a level of performance consistent with inter observer variation. However, conventional training procedures frequently depend on pixel-wise loss functions, limiting optimisation with respect to extended or global features. As a result, inferred segmentations can lack spatial coherence, including spurious connected components or holes. Such results are implausible, violating the anticipated topology of image segments, which is frequently known a priori. Addressing this challenge, published work has employed persistent homology, constructing topological loss functions for the evaluation of image segments against an explicit prior. Building a richer description of segmentation topology by considering all possible labels and label pairs, we extend these losses to the task of multi-class segmentation. These topological priors allow us to resolve all topological errors in a subset of 150 examples from the ACDC short axis CMR training data set, without sacrificing overlap performance.

Ozsel Kilinc, Giovanni Montana

Learning robot manipulation through deep reinforcement learning in environments with sparse rewards is a challenging task. In this paper we address this problem by introducing a notion of imaginary object goals. For a given manipulation task, the object of interest is first trained to reach a desired target position on its own, without being manipulated, through physically realistic simulations. The object policy is then leveraged to build a predictive model of plausible object trajectories providing the robot with a curriculum of incrementally more difficult object goals to reach during training. The proposed algorithm, Follow the Object (FO), has been evaluated on 7 MuJoCo environments requiring increasing degree of exploration, and has achieved higher success rates compared to alternative algorithms. In particularly challenging learning scenarios, e.g. where the object's initial and target positions are far apart, our approach can still learn a policy whereas competing methods currently fail.

Henry Charlesworth, Giovanni Montana

Learning with sparse rewards remains a significant challenge in reinforcement learning (RL), especially when the aim is to train a policy capable of achieving multiple different goals. To date, the most successful approaches for dealing with multi-goal, sparse reward environments have been model-free RL algorithms. In this work we propose PlanGAN, a model-based algorithm specifically designed for solving multi-goal tasks in environments with sparse rewards. Our method builds on the fact that any trajectory of experience collected by an agent contains useful information about how to achieve the goals observed during that trajectory. We use this to train an ensemble of conditional generative models (GANs) to generate plausible trajectories that lead the agent from its current state towards a specified goal. We then combine these imagined trajectories into a novel planning algorithm in order to achieve the desired goal as efficiently as possible. The performance of PlanGAN has been tested on a number of robotic navigation/manipulation tasks in comparison with a range of model-free reinforcement learning baselines, including Hindsight Experience Replay. Our studies indicate that PlanGAN can achieve comparable performance whilst being around 4-8 times more sample efficient.

Saad Mohamad, Giovanni Montana

Policy gradient reinforcement learning (RL) algorithms have achieved impressive performance in challenging learning tasks such as continuous control, but suffer from high sample complexity. Experience replay is a commonly used approach to improve sample efficiency, but gradient estimators using past trajectories typically have high variance. Existing sampling strategies for experience replay like uniform sampling or prioritised experience replay do not explicitly try to control the variance of the gradient estimates. In this paper, we propose an online learning algorithm, adaptive experience selection (AES), to adaptively learn an experience sampling distribution that explicitly minimises this variance. Using a regret minimisation approach, AES iteratively updates the experience sampling distribution to match the performance of a competitor distribution assumed to have optimal variance. Sample non-stationarity is addressed by proposing a dynamic (i.e. time changing) competitor distribution for which a closed-form solution is proposed. We demonstrate that AES is a low-regret algorithm with reasonable sample complexity. Empirically, AES has been implemented for deep deterministic policy gradient and soft actor critic algorithms, and tested on 8 continuous control tasks from the OpenAI Gym library. Ours results show that AES leads to significantly improved performance compared to currently available experience sampling strategies for policy gradient.

Emanuele Pesce, Giovanni Montana

In artificial multi-agent systems, the ability to learn collaborative policies is predicated upon the agents' communication skills: they must be able to encode the information received from the environment and learn how to share it with other agents as required by the task at hand. We present a deep reinforcement learning approach, Connectivity Driven Communication (CDC), that facilitates the emergence of multi-agent collaborative behaviour only through experience. The agents are modelled as nodes of a weighted graph whose state-dependent edges encode pair-wise messages that can be exchanged. We introduce a graph-dependent attention mechanisms that controls how the agents' incoming messages are weighted. This mechanism takes into full account the current state of the system as represented by the graph, and builds upon a diffusion process that captures how the information flows on the graph. The graph topology is not assumed to be known a priori, but depends dynamically on the agents' observations, and is learnt concurrently with the attention mechanism and policy in an end-to-end fashion. Our empirical results show that CDC is able to learn effective collaborative policies and can over-perform competing learning algorithms on cooperative navigation tasks.

Ozsel Kilinc, Giovanni Montana

Mastering robotic manipulation skills through reinforcement learning (RL) typically requires the design of shaped reward functions. Recent developments in this area have demonstrated that using sparse rewards, i.e. rewarding the agent only when the task has been successfully completed, can lead to better policies. However, state-action space exploration is more difficult in this case. Recent RL approaches to learning with sparse rewards have leveraged high-quality human demonstrations for the task, but these can be costly, time consuming or even impossible to obtain. In this paper, we propose a novel and effective approach that does not require human demonstrations. We observe that every robotic manipulation task could be seen as involving a locomotion task from the perspective of the object being manipulated, i.e. the object could learn how to reach a target state on its own. In order to exploit this idea, we introduce a framework whereby an object locomotion policy is initially obtained using a realistic physics simulator. This policy is then used to generate auxiliary rewards, called simulated locomotion demonstration rewards (SLDRs), which enable us to learn the robot manipulation policy. The proposed approach has been evaluated on 13 tasks of increasing complexity, and can achieve higher success rate and faster learning rates compared to alternative algorithms. SLDRs are especially beneficial for tasks like multi-object stacking and non-rigid object manipulation.

Nick Byrne, James R. Clough, Isra Valverde et al.

Patient-specific 3D printing of congenital heart anatomy demands an accurate segmentation of the thin tissue interfaces which characterise these diagnoses. Even when a label set has a high spatial overlap with the ground truth, inaccurate delineation of these interfaces can result in topological errors. These compromise the clinical utility of such models due to the anomalous appearance of defects. CNNs have achieved state-of-the-art performance in segmentation tasks. Whilst data augmentation has often played an important role, we show that conventional image resampling schemes used therein can introduce topological changes in the ground truth labelling of augmented samples. We present a novel pipeline to correct for these changes, using a fast-marching algorithm to enforce the topology of the ground truth labels within their augmented representations. In so doing, we invoke the idea of cardiac contiguous topology to describe an arbitrary combination of congenital heart defects and develop an associated, clinically meaningful metric to measure the topological correctness of segmentations. In a series of five-fold cross-validations, we demonstrate the performance gain produced by this pipeline and the relevance of topological considerations to the segmentation of congenital heart defects. We speculate as to the applicability of this approach to any segmentation task involving morphologically complex targets.

Yang Hu, Giovanni Montana

Transfer learning methods for reinforcement learning (RL) domains facilitate the acquisition of new skills using previously acquired knowledge. The vast majority of existing approaches assume that the agents have the same design, e.g. same shape and action spaces. In this paper we address the problem of transferring previously acquired skills amongst morphologically different agents (MDAs). For instance, assuming that a bipedal agent has been trained to move forward, could this skill be transferred on to a one-leg hopper so as to make its training process for the same task more sample efficient? We frame this problem as one of subspace learning whereby we aim to infer latent factors representing the control mechanism that is common between MDAs. We propose a novel paired variational encoder-decoder model, PVED, that disentangles the control of MDAs into shared and agent-specific factors. The shared factors are then leveraged for skill transfer using RL. Theoretically, we derive a theorem indicating how the performance of PVED depends on the shared factors and agent morphologies. Experimentally, PVED has been extensively validated on four MuJoCo environments. We demonstrate its performance compared to a state-of-the-art approach and several ablation cases, visualize and interpret the hidden factors, and identify avenues for future improvements.

Zhana Kuncheva, Giovanni Montana

The analysis of temporal networks has a wide area of applications in a world of technological advances. An important aspect of temporal network analysis is the discovery of community structures. Real data networks are often very large and the communities are observed to have a hierarchical structure referred to as multi-scale communities. Changes in the community structure over time might take place either at one scale or across all scales of the community structure. The multilayer formulation of the modularity maximization (MM) method introduced captures the changing multi-scale community structure of temporal networks. This method introduces a coupling between communities in neighboring time layers by allowing inter-layer connections, while different values of the resolution parameter enable the detection of multi-scale communities. However, the range of this parameter's values must be manually selected. When dealing with real life data, communities at one or more scales can go undiscovered if appropriate parameter ranges are not selected. A novel Temporal Multi-scale Community Detection (TMSCD) method overcomes the obstacles mentioned above. This is achieved by using the spectral properties of the temporal network represented as a multilayer network. In this framework we select automatically the range of relevant scales within which multi-scale community partitions are sought.

Emanuele Pesce, Giovanni Montana

Deep reinforcement learning algorithms have recently been used to train multiple interacting agents in a centralised manner whilst keeping their execution decentralised. When the agents can only acquire partial observations and are faced with tasks requiring coordination and synchronisation skills, inter-agent communication plays an essential role. In this work, we propose a framework for multi-agent training using deep deterministic policy gradients that enables concurrent, end-to-end learning of an explicit communication protocol through a memory device. During training, the agents learn to perform read and write operations enabling them to infer a shared representation of the world. We empirically demonstrate that concurrent learning of the communication device and individual policies can improve inter-agent coordination and performance in small-scale systems. Our experimental results show that the proposed method achieves superior performance in scenarios with up to six agents. We illustrate how different communication patterns can emerge on six different tasks of increasing complexity. Furthermore, we study the effects of corrupting the communication channel, provide a visualisation of the time-varying memory content as the underlying task is being solved and validate the building blocks of the proposed memory device through ablation studies.

Ozsel Kilinc, Giovanni Montana

Multi-agent reinforcement learning systems aim to provide interacting agents with the ability to collaboratively learn and adapt to the behaviour of other agents. In many real-world applications, the agents can only acquire a partial view of the world. Here we consider a setting whereby most agents' observations are also extremely noisy, hence only weakly correlated to the true state of the environment. Under these circumstances, learning an optimal policy becomes particularly challenging, even in the unrealistic case that an agent's policy can be made conditional upon all other agents' observations. To overcome these difficulties, we propose a multi-agent deep deterministic policy gradient algorithm enhanced by a communication medium (MADDPG-M), which implements a two-level, concurrent learning mechanism. An agent's policy depends on its own private observations as well as those explicitly shared by others through a communication medium. At any given point in time, an agent must decide whether its private observations are sufficiently informative to be shared with others. However, our environments provide no explicit feedback informing an agent whether a communication action is beneficial, rather the communication policies must also be learned through experience concurrently to the main policies. Our experimental results demonstrate that the algorithm performs well in six highly non-stationary environments of progressively higher complexity, and offers substantial performance gains compared to the baselines.

Nicoló Savioli, Miguel Silva Vieira, Pablo Lamata et al.

The clinical management of several cardiovascular conditions, such as pulmonary hypertension, require the assessment of the right ventricular (RV) function. This work addresses the fully automatic and robust access to one of the key RV biomarkers, its ejection fraction, from the gold standard imaging modality, MRI. The problem becomes the accurate segmentation of the RV blood pool from cine MRI sequences. This work proposes a solution based on Fully Convolutional Neural Networks (FCNN), where our first contribution is the optimal combination of three concepts (the convolution Gated Recurrent Units (GRU), the Generative Adversarial Networks (GAN), and the L1 loss function) that achieves an improvement of 0.05 and 3.49 mm in Dice Index and Hausdorff Distance respectively with respect to the baseline FCNN. This improvement is then doubled by our second contribution, the ROI-GAN, that sets two GANs to cooperate working at two fields of view of the image, its full resolution and the region of interest (ROI). Our rationale here is to better guide the FCNN learning by combining global (full resolution) and local Region Of Interest (ROI) features. The study is conducted in a large in-house dataset of $\sim$ 23.000 segmented MRI slices, and its generality is verified in a publicly available dataset.

Nicoló Savioli, Miguel Silva Vieira, Pablo Lamata et al.

The segmentation of the left ventricle (LV) from CINE MRI images is essential to infer important clinical parameters. Typically, machine learning algorithms for automated LV segmentation use annotated contours from only two cardiac phases, diastole, and systole. In this work, we present an analysis work-flow for fully-automated LV segmentation that learns from images acquired through the cardiac cycle. The workflow consists of three components: first, for each image in the sequence, we perform an automated localization and subsequent cropping of the bounding box containing the cardiac silhouette. Second, we identify the LV contours using a Temporal Fully Convolutional Neural Network (T-FCNN), which extends Fully Convolutional Neural Networks (FCNN) through a recurrent mechanism enforcing temporal coherence across consecutive frames. Finally, we further defined the boundaries using either one of two components: fully-connected Conditional Random Fields (CRFs) with Gaussian edge potentials and Semantic Flow. Our initial experiments suggest that significant improvement in performance can potentially be achieved by using a recurrent neural network component that explicitly learns cardiac motion patterns whilst performing LV segmentation.

Nicoló Savioli, Giovanni Montana, Pablo Lamata

Atrial Fibrillation (AF) is a common electro-physiological cardiac disorder that causes changes in the anatomy of the atria. A better characterization of these changes is desirable for the definition of clinical biomarkers, furthermore, thus there is a need for its fully automatic segmentation from clinical images. In this work, we present an architecture based on 3D-convolution kernels, a Volumetric Fully Convolution Neural Network (V-FCNN), able to segment the entire volume in a one-shot, and consequently integrate the implicit spatial redundancy present in high-resolution images. A loss function based on the mixture of both Mean Square Error (MSE) and Dice Loss (DL) is used, in an attempt to combine the ability to capture the bulk shape as well as the reduction of local errors products by over-segmentation. Results demonstrate a reasonable performance in the middle region of the atria along with the impact of the challenges of capturing the variability of the pulmonary veins or the identification of the valve plane that separates the atria to the ventricle. A final dice of $92.5\%$ in $54$ patients ($4752$ atria test slices in total) is shown.

Ruggiero Santeramo, Samuel Withey, Giovanni Montana

Convolutional neural networks (CNNs) have been successfully employed in recent years for the detection of radiological abnormalities in medical images such as plain x-rays. To date, most studies use CNNs on individual examinations in isolation and discard previously available clinical information. In this study we set out to explore whether Long-Short-Term-Memory networks (LSTMs) can be used to improve classification performance when modelling the entire sequence of radiographs that may be available for a given patient, including their reports. A limitation of traditional LSTMs, though, is that they implicitly assume equally-spaced observations, whereas the radiological exams are event-based, and therefore irregularly sampled. Using both a simulated dataset and a large-scale chest x-ray dataset, we demonstrate that a simple modification of the LSTM architecture, which explicitly takes into account the time lag between consecutive observations, can boost classification performance. Our empirical results demonstrate improved detection of commonly reported abnormalities on chest x-rays such as cardiomegaly, consolidation, pleural effusion and hiatus hernia.

Nicolo' Savioli, Silvia Visentin, Erich Cosmi et al.

The automatic analysis of ultrasound sequences can substantially improve the efficiency of clinical diagnosis. In this work we present our attempt to automate the challenging task of measuring the vascular diameter of the fetal abdominal aorta from ultrasound images. We propose a neural network architecture consisting of three blocks: a convolutional layer for the extraction of imaging features, a Convolution Gated Recurrent Unit (C-GRU) for enforcing the temporal coherence across video frames and exploiting the temporal redundancy of a signal, and a regularized loss function, called \textit{CyclicLoss}, to impose our prior knowledge about the periodicity of the observed signal. We present experimental evidence suggesting that the proposed architecture can reach an accuracy substantially superior to previously proposed methods, providing an average reduction of the mean squared error from $0.31 mm^2$ (state-of-art) to $0.09 mm^2$, and a relative error reduction from $8.1\%$ to $5.3\%$. The mean execution speed of the proposed approach of 289 frames per second makes it suitable for real time clinical use.

Mauro Annarumma, Giovanni Montana

Many radiological studies can reveal the presence of several co-existing abnormalities, each one represented by a distinct visual pattern. In this article we address the problem of learning a distance metric for plain radiographs that captures a notion of "radiological similarity": two chest radiographs are considered to be similar if they share similar abnormalities. Deep convolutional neural networks (DCNs) are used to learn a low-dimensional embedding for the radiographs that is equipped with the desired metric. Two loss functions are proposed to deal with multi-labelled images and potentially noisy labels. We report on a large-scale study involving over 745,000 chest radiographs whose labels were automatically extracted from free-text radiological reports through a natural language processing system. Using 4,500 validated exams, we demonstrate that the methodology performs satisfactorily on clustering and image retrieval tasks. Remarkably, the learned metric separates normal exams from those having radiological abnormalities.

Emanuele Pesce, Petros-Pavlos Ypsilantis, Samuel Withey et al.

Machine learning approaches hold great potential for the automated detection of lung nodules in chest radiographs, but training the algorithms requires vary large amounts of manually annotated images, which are difficult to obtain. Weak labels indicating whether a radiograph is likely to contain pulmonary nodules are typically easier to obtain at scale by parsing historical free-text radiological reports associated to the radiographs. Using a repositotory of over 700,000 chest radiographs, in this study we demonstrate that promising nodule detection performance can be achieved using weak labels through convolutional neural networks for radiograph classification. We propose two network architectures for the classification of images likely to contain pulmonary nodules using both weak labels and manually-delineated bounding boxes, when these are available. Annotated nodules are used at training time to deliver a visual attention mechanism informing the model about its localisation performance. The first architecture extracts saliency maps from high-level convolutional layers and compares the estimated position of a nodule against the ground truth, when this is available. A corresponding localisation error is then back-propagated along with the softmax classification error. The second approach consists of a recurrent attention model that learns to observe a short sequence of smaller image portions through reinforcement learning. When a nodule annotation is available at training time, the reward function is modified accordingly so that exploring portions of the radiographs away from a nodule incurs a larger penalty. Our empirical results demonstrate the potential advantages of these architectures in comparison to competing methodologies.

Dimosthenis Tsagkrasoulis, Giovanni Montana

An increasing array of biomedical and computer vision applications requires the predictive modeling of complex data, for example images and shapes. The main challenge when predicting such objects lies in the fact that they do not comply to the assumptions of Euclidean geometry. Rather, they occupy non-linear spaces, a.k.a. manifolds, where it is difficult to define concepts such as coordinates, vectors and expected values. In this work, we construct a non-parametric predictive methodology for manifold-valued objects, based on a distance modification of the Random Forest algorithm. Our method is versatile and can be applied both in cases where the response space is a well-defined manifold, but also when such knowledge is not available. Model fitting and prediction phases only require the definition of a suitable distance function for the observed responses. We validate our methodology using simulations and apply it on a series of illustrative image completion applications, showcasing superior predictive performance, compared to various established regression methods.

Petros-Pavlos Ypsilantis, Giovanni Montana

X-rays are commonly performed imaging tests that use small amounts of radiation to produce pictures of the organs, tissues, and bones of the body. X-rays of the chest are used to detect abnormalities or diseases of the airways, blood vessels, bones, heart, and lungs. In this work we present a stochastic attention-based model that is capable of learning what regions within a chest X-ray scan should be visually explored in order to conclude that the scan contains a specific radiological abnormality. The proposed model is a recurrent neural network (RNN) that learns to sequentially sample the entire X-ray and focus only on informative areas that are likely to contain the relevant information. We report on experiments carried out with more than $100,000$ X-rays containing enlarged hearts or medical devices. The model has been trained using reinforcement learning methods to learn task-specific policies.

James H Cole, Rudra PK Poudel, Dimosthenis Tsagkrasoulis et al.

Machine learning analysis of neuroimaging data can accurately predict chronological age in healthy people and deviations from healthy brain ageing have been associated with cognitive impairment and disease. Here we sought to further establish the credentials of "brain-predicted age" as a biomarker of individual differences in the brain ageing process, using a predictive modelling approach based on deep learning, and specifically convolutional neural networks (CNN), and applied to both pre-processed and raw T1-weighted MRI data. Firstly, we aimed to demonstrate the accuracy of CNN brain-predicted age using a large dataset of healthy adults (N = 2001). Next, we sought to establish the heritability of brain-predicted age using a sample of monozygotic and dizygotic female twins (N = 62). Thirdly, we examined the test-retest and multi-centre reliability of brain-predicted age using two samples (within-scanner N = 20; between-scanner N = 11). CNN brain-predicted ages were generated and compared to a Gaussian Process Regression (GPR) approach, on all datasets. Input data were grey matter (GM) or white matter (WM) volumetric maps generated by Statistical Parametric Mapping (SPM) or raw data. Brain-predicted age represents an accurate, highly reliable and genetically-valid phenotype, that has potential to be used as a biomarker of brain ageing. Moreover, age predictions can be accurately generated on raw T1-MRI data, substantially reducing computation time for novel data, bringing the process closer to giving real-time information on brain health in clinical settings.

Ricardo Pio Monti, Christoforos Anagnostopoulos, Giovanni Montana

Large scale, streaming datasets are ubiquitous in modern machine learning. Streaming algorithms must be scalable, amenable to incremental training and robust to the presence of non-stationarity. In this work consider the problem of learning $\ell_1$ regularized linear models in the context of streaming data. In particular, the focus of this work revolves around how to select the regularization parameter when data arrives sequentially and the underlying distribution is non-stationary (implying the choice of optimal regularization parameter is itself time-varying). We propose a framework through which to infer an adaptive regularization parameter. Our approach employs an $\ell_1$ penalty constraint where the corresponding sparsity parameter is iteratively updated via stochastic gradient descent. This serves to reformulate the choice of regularization parameter in a principled framework for online learning. The proposed method is derived for linear regression and subsequently extended to generalized linear models. We validate our approach using simulated and real datasets and present an application to a neuroimaging dataset.