Agentified Assessment of Logical Reasoning Agents

We present a framework for evaluating and benchmarking logical reasoning agents when assessment itself must be reproducible, auditable, and robust to execution failures. Building on agentified assessment, we use an assessor agent to issue tasks, enforce execution budgets, parse outputs, and record structured failure types, while the agent under test only needs to expose a standardized agent-to-agent interface. As a case study, we benchmark an auto-formalization agent for first-order logic (FOL) reasoning on a solver-verified and repaired split of FOLIO. The agent translates natural language premises and conclusions into executable Z3Py programs and employs satisfiability modulo theories (SMT) solving to determine logical entailment. On the cleaned FOLIO validation set, the auto-formalization agent achieves 86.70% accuracy under the assessor protocol, outperforming a chain-of-thought baseline (73.89%).

First-order methods for stochastic and finite-sum convex optimization with deterministic constraints

In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which the expected constraint violation and expected optimality gap are both within a prescribed tolerance $\epsilon$. However, in many practical applications, constraints must be nearly satisfied with certainty, rendering such solutions potentially unsuitable due to the risk of substantial violations. To address this issue, we propose stochastic first-order methods for finding an $\epsilon$-$surely\ feasible\ stochastic\ optimal$ ($\epsilon$-SFSO) solution, where the constraint violation is deterministically bounded by $\epsilon$ and the expected optimality gap is at most $\epsilon$. Our methods apply an accelerated stochastic gradient (ASG) scheme or a modified variance-reduced ASG scheme $only\ once$ to a sequence of quadratic penalty subproblems with appropriately chosen penalty parameters. We establish first-order oracle complexity bounds for the proposed methods in computing an $\epsilon$-SFSO solution. As a byproduct, we also derive first-order oracle complexity results for sample average approximation method in computing an $\epsilon$-SFSO solution of the stochastic optimization problem using our proposed methods to solve the sample average problem.

Variance-reduced first-order methods for deterministically constrained stochastic nonconvex optimization with strong convergence guarantees

In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an $\epsilon$-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy $\epsilon$. However, in many practical applications, it is crucial that the constraints be nearly satisfied with certainty, making such an $\epsilon$-stochastic stationary point potentially undesirable due to the risk of significant constraint violations. To address this issue, we propose single-loop variance-reduced stochastic first-order methods, where the stochastic gradient of the stochastic component is computed using either a truncated recursive momentum scheme or a truncated Polyak momentum scheme for variance reduction, while the gradient of the deterministic component is computed exactly. Under the error bound condition with a parameter $\theta \geq 1$ and other suitable assumptions, we establish that the proposed methods achieve a sample complexity and first-order operation complexity of $\widetilde O(\epsilon^{-\max\{4, 2\theta\}})$ for finding a stronger $\epsilon$-stochastic stationary point, where the constraint violation is within $\epsilon$ with certainty, and the expected violation of first-order stationarity is within $\epsilon$. To the best of our knowledge, this is the first work to develop methods with provable complexity guarantees for finding an approximate stochastic stationary point of such problems that nearly satisfies all constraints with certainty.