Push-Sum-based decentralized learning enables optimization over directed communication networks, where information exchange may be asymmetric. While convergence properties of such methods are well understood, their finite-iteration stability and generalization behavior remain unclear due to structural bias induced by column-stochastic mixing and asymmetric error propagation. In this work, we develop a unified uniform-stability framework for the Stochastic Gradient Push (SGP) algorithm that captures the effect of directed topology. A key technical ingredient is an imbalance-aware consistency bound for Push-Sum, which controls consensus deviation through two quantities: the stationary distribution imbalance parameter $δ$ and the spectral gap $(1-λ)$ governing mixing speed. This decomposition enables us to disentangle statistical effects from topology-induced bias. We establish finite-iteration stability and optimization guarantees for both convex objectives and non-convex objectives satisfying the Polyak--Łojasiewicz condition. For convex problems, SGP attains excess generalization error of order $\tilde{\mathcal{O}}\!\left(\frac{1}{\sqrt{mn}}+\fracγ{δ(1-λ)}+γ\right)$ under step-size schedules, and we characterize the corresponding optimal early stopping time that minimizes this bound. For PŁ objectives, we obtain convex-like optimization and generalization rates with dominant dependence proportional to $κ\!\left(1+\frac{1}{δ(1-λ)}\right)$, revealing a multiplicative coupling between problem conditioning and directed communication topology. Our analysis clarifies when Push-Sum correction is necessary compared with standard decentralized SGD and quantifies how imbalance and mixing jointly shape the best attainable learning performance.

Instead of relying on the LLM itself to unlearn, we enforce an unlearned state during inference by employing a prompt classifier to identify and safeguard prompts to forget.

For this reason, the ML community started focusing on non-monotone problems with extra structural properties.

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Their Markovian structure makes it difficult to define DDPMs with distributions other than Gaussian or discrete. In this paper, we introduce Star-Shaped DDPM (SS-DDPM).

In this setting, methods are widely used since they come with several advantages when dealing with continuous-control problems. These methods search in the policy space with an or exploration strategy, depending on whether they learn directly the parameters of a stochastic policy or those of a stochastic hyperpolicy. In this paper, we propose a general framework for addressing CRL problems via algorithms, relying on an alternate ascent/descent scheme with dual-variable regularization. We introduce an exploration-agnostic algorithm, called C-PG, which exhibits global last-iterate convergence guarantees under (weak) gradient domination assumptions, improving and generalizing existing results. Then, we design C-PGAE and C-PGPE, the action-based and the parameter-based versions of C-PG, respectively, and we illustrate how they naturally extend to constraints defined in terms of over the costs, as it is often requested in safety-critical scenarios. Finally, we numerically validate our algorithms on constrained control problems, and compare them with state-of-the-art baselines, demonstrating their effectiveness.