Conformal Sequential Decision Making With Cost and Sublinear Policy Regret Guarantees
Authors: Jayadev Naram, Giuseppe Durisi, Matteo Zecchin, Osvaldo Simeone
Organizations: Department of Electrical Engineering, Chalmers University of Technology, 412 96 Göteborg, Sweden · Communication Systems Department, EURECOM, 06410 Sophia Antipolis, France · Institute for Intelligent Networked Systems (INSI), Northeastern University London, E1W 1LP London, UK
Automated decision makers, such as AI agents that control robots or network devices, must often satisfy hard cost constraints while maintaining competitive performance. In such settings, a cost measure, such as a safety violation rate, energy consumption, or a distortion level, must stay within a given budget in every episode of operation. Furthermore, a cumulative reward metric, accounting for per-step performance, must stay close to the reward of a meaningful reference policy. We formulate this setup as an episodic sequential decision problem in which the state sequence is arbitrary, and the reward and cost may depend on past actions within the same episode. We propose the online conformal episodic agent (OCEA), a policy that selects one candidate action per episode using a regret-controlled algorithm, and switches to a zero-cost action when the remaining budget cannot absorb the maximum cost of one more round. We prove that OCEA satisfies per-episode cost constraints for every state sequence and for every realization of its internal randomness, while achieving a sublinear expected policy regret with respect to the best action sequence in hindsight from a comparator class satisfying the same per-episode cost constraints. We apply OCEA to risk-averse control and online compression with distortion guarantees.
Figures & tables
Fig. 1: Normalized policy regret as a function of the time horizon T for OCSC and OCEA. The dashed line indicates the OCSC regret lower bound 41log2(968/675) . The OCEA curve corresponds to the mean over 128 independent runs, with error bars showing one standard deviation.
We study risk-averse decision making, in which an agent selects actions while being uncertain about the true system state. The risk is measured via optimized certainty equivalent (OCE) metrics, which generalize popular criteria such as mean-variance risk and conditional value-at-risk (CVaR). We characterize the optimal policy under known distributions, and show that it reduces to a prediction set-based solution for the CVaR. This provides an operational interpretation of conformal prediction-type prediction sets. For unknown distributions, we develop a data-driven calibration strategy, based on a synthetic model for the likelihood and held-out calibration data, yielding high-probability control of the OCE risk. The approach is evaluated on two wireless beamforming settings.
Amirmohammad Farzaneh, Osvaldo Simeone
Institute for Intelligent Networked Systems (INSI), Northeastern University London, London, UK
We address the problem of conformal selection, where an agent must select a minimal subset of options to ensure that at least one success'' is identified with a pre-specified target probability $φ$. While traditional online conformal prediction focuses on maintaining validity for the observed sequence, minimizing the resource cost (efficiency) of such selections, especially under limited feedback, remains a significant challenge. In this work, we consider settings with the most limited bandit'' feedback, and demonstrate that the simple Adaptive Conformal Inference (ACI) update rule, when applied to the appropriate control parameter or dual variable, is both adversarially valid, ensuring the success target is met on average for any input sequence (and hence under distribution shifts), and stochastically efficient, achieving sublinear efficiency regret for i.i.d. inputs against an appropriate stochastic benchmark. We show such guarantees under canonical models capturing bandit and semi-bandit feedback to the agent via a unifying algorithmic technique, and analytic framework involving Lyapunov functions. Our approach handles more complex settings than prior work, while requiring significantly less feedback, and our results provide a new theoretical bridge between efficient online learning with limited feedback and distribution-free uncertainty quantification.
We study Constrained Online Convex Optimization with Memory (COCO-M), where both the loss and the constraints depend on a finite window of past decisions made by the learner. This setting extends the previously studied unconstrained online optimization with memory framework and captures practical problems such as the control of constrained dynamical systems and scheduling with reconfiguration budgets. For this problem, we propose the first algorithms that achieve sublinear regret and sublinear cumulative constraint violation under time-varying constraints, both with and without predictions of future loss and constraint functions. Without predictions, we introduce an adaptive penalty approach that guarantees sublinear regret and constraint violation. When short-horizon and potentially unreliable predictions are available, we reinterpret the problem as online learning with delayed feedback and design an optimistic algorithm whose performance improves as prediction accuracy improves, while remaining robust when predictions are inaccurate. Our results bridge the gap between classical constrained online convex optimization and memory-dependent settings, and provide a versatile learning toolbox with diverse applications.
Mohammed Abdullah, George Iosifidis, Salah Eddine Elayoubi +1
Université Paris-Saclay, CentraleSupélec, CNRS, L2S, Gif-sur-Yvette, France · Institut Polytechnique de Paris, Télécom SudParis, Palaiseau, France · Delft University of Technology, The Netherlands