arXiv subjects

Jonas Gillberg

Publications and source records attributed to Jonas Gillberg.

3 recordsLinked to original sources

arXiv2026

A kernel proof of the De Cock-De Moor Lyapunov identity

We prove the rank-one Lyapunov spectral identity recorded as Problem 9.1 in the 2004 collection of unsolved problems in mathematical systems and control theory. Let $P,Q,R$ solve the coupled discrete Lyapunov and Sylvester equations associated with $A$ and its rank-one update $A_2=A+vw^\top$. When the displayed inverses exist, we show that $P^{-1}RQ^{-1}R^\top$ and $(I+PQ)^{-1}$ have the same characteristic polynomial. A rank-one determinant factorization of the equation for $Q$ produces a scalar bilinear kernel. Evaluating it at the eigenvalues of $A$ and at their reciprocals gives $RQ^{-1}R^\top=BQ^{-1}B=P-BPB$, after which the two target matrices are the same two factors in opposite order. Polynomial continuation extends the identity from a nonempty open set of admissible systems to the full admissible domain and yields a determinant corollary without stability assumptions; when the spectra of $A$ and $A_2$ are disjoint, $Z=b(A)^{-1}P$ gives an explicit similarity. In the Schur-stable realization setting, the result recovers the associated principal-angle and past/future canonical-correlation spectra.

eess.SY↗

arXiv2024

Improving Conditional Level Generation using Automated Validation in Match-3 Games

Generative models for level generation have shown great potential in game production. However, they often provide limited control over the generation, and the validity of the generated levels is unreliable. Despite this fact, only a few approaches that learn from existing data provide the users with ways of controlling the generation, simultaneously addressing the generation of unsolvable levels. %One of the main challenges it faces is that levels generated through automation may not be solvable thus requiring validation. are not always engaging, challenging, or even solvable. This paper proposes Avalon, a novel method to improve models that learn from existing level designs using difficulty statistics extracted from gameplay. In particular, we use a conditional variational autoencoder to generate layouts for match-3 levels, conditioning the model on pre-collected statistics such as game mechanics like difficulty and relevant visual features like size and symmetry. Our method is general enough that multiple approaches could potentially be used to generate these statistics. We quantitatively evaluate our approach by comparing it to an ablated model without difficulty conditioning. Additionally, we analyze both quantitatively and qualitatively whether the style of the dataset is preserved in the generated levels. Our approach generates more valid levels than the same method without difficulty conditioning.

cs.LG↗

arXiv2023

Technical Challenges of Deploying Reinforcement Learning Agents for Game Testing in AAA Games

Going from research to production, especially for large and complex software systems, is fundamentally a hard problem. In large-scale game production, one of the main reasons is that the development environment can be very different from the final product. In this technical paper we describe an effort to add an experimental reinforcement learning system to an existing automated game testing solution based on scripted bots in order to increase its capacity. We report on how this reinforcement learning system was integrated with the aim to increase test coverage similar to [1] in a set of AAA games including Battlefield 2042 and Dead Space (2023). The aim of this technical paper is to show a use-case of leveraging reinforcement learning in game production and cover some of the largest time sinks anyone who wants to make the same journey for their game may encounter. Furthermore, to help the game industry to adopt this technology faster, we propose a few research directions that we believe will be valuable and necessary for making machine learning, and especially reinforcement learning, an effective tool in game production.

cs.SE↗