arXiv subjects

Rafał Wisniewski

Publications and source records attributed to Rafał Wisniewski.

6 recordsLinked to original sources

arXiv2025

Deflating quantum error-correcting codes

In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases where more than a single qudit is removed. We show that the parameters of the deflated quantum code can be controlled, and argue that a similar approach is not as beneficial when applied to classical linear codes. Furthermore, it is shown that deflation introduces additional freedom compared to applying just puncturing and shortening consecutively. We exemplify that it is possible to obtain better parameters by deflating a code rather than consecutively using puncturing and shortening.

quant-ph↗

arXiv2025

An Online Multiobjective Policy Gradient for Long-run Average-reward Markov Decision Process

We propose a reinforcement learning (RL) framework for multi-objective decision-making, where the agent seeks to optimize a vector of rewards rather than a single scalar value. The objective is to ensure that the time-averaged reward vector converges asymptotically to a predefined target set. Since standard RL algorithms operate on scalar rewards, we introduce a dynamic scalarization mechanism guided by Blackwell's Approachability Theorem. This theorem enables adaptive updates of the scalarization vector to guarantee convergence toward the target set. Assuming ergodicity, the Markov chain induced by the learned policies admits a stationary distribution, ensuring all states recur with finite return times. Our algorithm exploits this property by defining an inner loop that applies a policy gradient method (with baseline) between successive visits to a designated recurrent state, enforcing Blackwell's condition at each iteration. An outer loop then updates the scalarization vector after each recurrence. We establish theoretical convergence of the long-run average reward vector to the target set and validate the approach through a numerical example.

eess.SY↗

arXiv2025

Robust Correlated Equilibrium: Definition and Computation

We study N-player finite games with costs perturbed due to time-varying disturbances in the underlying system and to that end, we propose the concept of Robust Correlated Equilibrium that generalizes the definition of Correlated Equilibrium. Conditions under which the Robust Correlated Equilibrium exists are specified, and a decentralized algorithm for learning strategies that are optimal in the sense of Robust Correlated Equilibrium is proposed. The primary contribution of the paper is the convergence analysis of the algorithm and to that end, we propose a modification of the celebrated Blackwell's Approachability theorem to games with costs that are not just time-average, as in the original Blackwell's Approachability Theorem, but also include the time-average of previous algorithm iterates. The designed algorithm is applied to a practical water distribution network with pumps being the controllers and their costs being perturbed by uncertain consumption due to the consumers. Simulation results show that each controller achieves no regret, and empirical distributions converge to the Robust Correlated Equilibrium.

eess.SY↗

arXiv2025

Puncturing Quantum Stabilizer Codes

Classical coding theory contains several techniques to obtain new codes from other codes, including puncturing and shortening. For quantum codes, a form of puncturing is known, but its description is based on the code space rather than its generators. In this work, we generalize the puncturing procedure to allow more freedom in the choice of which coded states are kept and which are removed. We describe this puncturing by focusing on the stabilizer matrix containing the generators of the code. In this way, we are able to explicitly describe the stabilizer matrix of the punctured code given the stabilizer matrix of the original stabilizer code. The additional freedom in the procedure also opens up new ways to construct new codes from old, and we present several ways to utilize this for the search of codes with good or even optimal parameters. In particular, we use the construction to obtain codes whose parameters exceed the best previously known. Lastly, we generalize the proof of the Griesmer bound from the classical setting to stabilizer codes since the proof relies heavily on the puncturing technique.

cs.IT↗

arXiv2023

On Bellman's principle of optimality and Reinforcement learning for safety-constrained Markov decision process

We study optimality for the safety-constrained Markov decision process which is the underlying framework for safe reinforcement learning. Specifically, we consider a constrained Markov decision process (with finite states and finite actions) where the goal of the decision maker is to reach a target set while avoiding an unsafe set(s) with certain probabilistic guarantees. Therefore the underlying Markov chain for any control policy will be multichain since by definition there exists a target set and an unsafe set. The decision maker also has to be optimal (with respect to a cost function) while navigating to the target set. This gives rise to a multi-objective optimization problem. We highlight the fact that Bellman's principle of optimality may not hold for constrained Markov decision problems with an underlying multichain structure (as shown by the counterexample due to Haviv. We resolve the counterexample by formulating the aforementioned multi-objective optimization problem as a zero-sum game and thereafter construct an asynchronous value iteration scheme for the Lagrangian (similar to Shapley's algorithm). Finally, we consider the reinforcement learning problem for the same and construct a modified $Q$-learning algorithm for learning the Lagrangian from data. We also provide a lower bound on the number of iterations required for learning the Lagrangian and corresponding error bounds.

eess.SY↗

arXiv2021

Algebraic Test for Asymptotic Stability of Periodic Orbits for Polynomial Systems

We will address the problem of determining the existence and asymptotic stability of a non-trivial periodic orbit in dynamical systems described by polynomial vector fields. To this end, we will lean upon the celebrated results of Borg, Olech and Hartman and newer results of Giesl, who all employ the concept of contraction for this purpose. Importantly, we formulate a numerically tractable algebraic test. The developed algorithm is illustrated in a numerical example.

math.DS↗