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Junhao Shen

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11works
4topics
4close collaborators

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11 publications

preprint2026arXiv

Dynamic Skill Lifecycle Management for Agentic Reinforcement Learning

Large language model agents increasingly rely on external skills to solve complex tasks, where skills act as modular units that extend their capabilities beyond what parametric memory alone supports. Existing methods assume external skills either accumulate as persistent guidance or internalized into the policy, eventually leading to zero-skill inference. We argue this assumption is overly restrictive, since with limited parametric capacity and uneven marginal contribution across skills, the optimal active skill set is non-monotonic, task- and stage-dependent. In this work, we propose SLIM, a framework of dynamic Skill LIfecycle Management for agentic reinforcement learning (RL), which treats the active external skill set as a dynamic optimization variable jointly updated with policy learning. Specifically, SLIM estimates each active skill's marginal external contribution through leave-one-skill-out validation, then applies three lifecycle operations: retaining high-value skills, retiring skills whose contribution becomes negligible after sufficient exposure, and expanding the skill bank when persistent failures reveal missing capability coverage. Experiments show that SLIM outperforms the best baselines by an average of 7.1% points across ALFWorld and SearchQA. Results further indicate that policy learning and external skill retention are not mutually exclusive: some skills are absorbed into the policy, while others continue to provide external value, supporting SLIM as a more general paradigm for skill-based agentic RL.

preprint2015arXiv

A non-commutative Beurling's theorem with respect to unitarily invariant norms

In 1967, Arveson invented a non-commutative generalization of classical H∞,H^{\infty}, known as finite maximal subdiagonal subalgebras, for a finite von Neumann algebra M\mathcal M with a faithful normal tracial state ττ. In 2008, Blecher and Labuschagne proved a version of Beurling's theorem on H∞H^\infty-right invariant subspaces in a non-commutative Lp(M,τ)L^{p}(\mathcal M,τ) space for 1≤p≤∞1\le p\le \infty. In the present paper, we define and study a class of norms Nc(M,τ){\mathcal{N}}_{c}(\mathcal M, τ) on M,\mathcal{M}, called normalized, unitarily invariant, ∥⋅∥1\Vert \cdot \Vert_{1}-dominating, continuous norms, which properly contains the class {∥⋅∥p:1≤p<∞}.\{ \Vert \cdot \Vert_{p}:1\leq p< \infty \}. For α∈Nc(M,τ),α\in \mathcal{N}_{c}(\mathcal M, τ), we define a non-commutative Lα(M,τ)L^{α}({\mathcal{M}},τ) space and a non-commutative HαH^α space. Then we obtain a version of the Blecher-Labuschagne-Beurling invariant subspace theorem on H∞H^\infty-right invariant subspaces in a non-commutative Lα(M,τ)L^{α}({\mathcal{M}},τ) space. Key ingredients in the proof of our main result include a characterization theorem of HαH^α and a density theorem for Lα(M,τ)L^α(\mathcal M,τ).

preprint2015arXiv

Similarity degree of a class of C∗^*-algebras

Suppose that M\mathcal M is a countably decomposable type II1_1 von Neumann algebra and A\mathcal A is a separable, non-nuclear, unital C∗^*-algebra. We show that, if M\mathcal M has Property ΓΓ, then the similarity degree of M\mathcal M is less than or equal to 55. If A\mathcal A has Property c∗^*-ΓΓ, then the similarity degree of A\mathcal A is equal to 33. In particular, the similarity degree of a Z\mathcal Z-stable, separable, non-nuclear, unital C∗^*-algebra is equal to 33.

preprint2014arXiv

A note on unital full amalgamated free products of quasi-diagonal C*-algebras

In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite dimensional C*- algebra is quasidiagonal. Applying this result, we conclude that a unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree.

preprint2014arXiv

Hochschild cohomology of type II1_1 von Neumann algebras with Property ΓΓ

In this paper, Property ΓΓ for a type II1_{1} von Neumann algebra is introduced as a generalization of Murray and von Neumann's Property ΓΓ for a type II1_{1} factor. The main result of this paper is that if a type II1_{1} von Neumann algebra M\mathcal{M} with separable predual has Property ΓΓ, then the continuous Hochschild cohomology group Hk(M,M)H^{k}(\mathcal{M}, \mathcal{M}) vanishes for every k≥2k \geq 2. This gives a generalization of an earlier result due to E. Christensen, F. Pop, A.M. Sinclair and R.R. Smith.

preprint2012arXiv

Approximate Double Commutants and Distance Formulas

We extend work of the first author concering relative double commutants and approximate double commutants of unital subalgebras of unital C*-algebras, including metric versions involving distance estimates. We prove metric results for AH subalgebras of von Neumann algebras or AF subalgebras of primitive C*-algebras. We prove other general results, including some for nonselfadjoint commutative subalgebras, using C*-algebraic versions of the Stone-Weierstrass and Bishop-Stone-Weierstrass theorems.

preprint2010arXiv

Unital Full Amalgamated Free Products of MF Algebras

In this paper, we consider the question whether a unital full free product of MF algebras with amalgamation over a finite dimensional C*-algebra is an MF algebra. First, we show that, under a natural condition, a unital full free product of two separable residually finite dimensional (RFD) C*-algebras with amalgamation over a finite dimensional C*-algebra is again a separable RFD C*-algebra. Applying this result on MF C*-algebras, we show that, under a natual condition, a unital full free product of two MF algebras is again an MF algebra. As an application, we show that a unital full free product of two AF algebras with amalgamation over an AF algebra is an MF algebra if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree.

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