arXiv subjects

Vaneet Aggarwal

Publications and source records attributed to Vaneet Aggarwal.

At least 37 records · Page 2Linked to original sources

arXiv2026

Selection-Aware Stress Testing for Interactive Agents

Agent evaluations often use one benchmark to choose a workflow and then search for task types where its advantage weakens, so both conclusions are selected from the same data. We introduce Selection-Aware Semantic Stress Testing (\SASST{}), which learns a task reweighting from pre-execution features on discovery tasks and evaluates the same paired comparison on separate confirmation tasks. The protocol checks support and stability, uses joint bounds for all planned claims, and can return no claim. We prove conditional asymptotic validity under stated cluster assumptions. A forty-cluster audit finds Gaussian undercoverage and conservative Bonferroni $t$ bounds. In one 480-episode $τ$-bench study, a $3.75$ point discovery gain vanished on confirmation. A second-model study likewise confirmed neither a workflow benefit nor a stable stress rule.

cs.LG↗

arXiv2026

BAGEL: Adversarially Constrained Online Convex Optimization under Separation Oracle Access

In adversarial Constrained Online Convex Optimization (COCO), a learner selects actions from a fixed convex set while seeking both low regret and low cumulative constraint violation (CCV) under time-varying constraints. We ask what performance is achievable when the action set is accessed through a Separation Oracle (SO), rather than an exact Projection Oracle (PO) or a Linear Optimization Oracle (LOO). We introduce $\mathtt{BAGEL}$, which combines a Lyapunov-weighted surrogate loss, blocked adaptive online gradient descent, and an infeasible-projection procedure implemented with an SO. For convex costs and any $β\in(0,1/2]$, $\mathtt{BAGEL}$ achieves $\mathcal{O}(T^{1-β})$ regret and $\mathcal{O}(T^{1-β}\log T)$ cumulative violation using $\widetilde{\mathcal{O}}((D/r)^2T^{2β})$ SO calls. At $β=1/2$, this gives $\mathcal{O}(\sqrt{T})$ regret and $\mathcal{O}(\sqrt{T}\log T)$ violation with a near-linear number of SO calls. The result is an access oracle based guarantee, with computational relevance depends on the geometry of the action set and the cost of implementing its SO.

cs.LG↗

arXiv2026

A Bi-directional Multi-solution Scalable Grover Search Algorithm

Grover's search algorithms, including various Partial Grover Searches (PGS), suffer from scaling issues when multiple solutions are sought, as the number of iterations scales with the number of solutions or marked states, making implementation more computationally expensive. Inspired by recent PGS algorithms for multi-solution searchers, this article proposes a scalable Grover quantum search algorithm, referred to as Bi-directional Multi-solution scalable Grover Search (BMGS), to efficiently search for an arbitrary number of solutions from an unstructured database. We introduced a novel multi-segment bidirectional search tactic with PGS across multiple equal segments of each state, starting from an initial state and multiple marked states in parallel, obviating the need for merge operations. We have shown in this work that for each solution our novel approach requires at most $\sqrt{\mathcal{N}}\left (1- \sqrt{\frac{1}{b^{\lfloor\frac{r}{dk}\rfloor}}}\right)$ iterations (here, $\mathcal{N}=2^r$ elements, $k=\log_2 b$, $d$ is the number of equal segments on $r$ qubits, and $b$ is the branching factor). Our proposed BMGS algorithm is benchmarked against state-of-the-art Depth First Grover Search (DFGS) and PGS implementations for an arbitrary number of solutions, ranging from $2$ to $20$ qubits, as a proof of concept. We also show that our BMGS requires fewer iterations for shallow quantum circuits and achieves an optimal $\mathcal{O}$($\sqrt{s\mathcal{N}}$) average complexity for $s$ solutions, when $dk < r$. The Qiskit Python implementation of the proposed BMGS algorithm is available on GitHub\footnote{https://anonymous.4open.science/r/Multi-Solution-DFGS-BMGS-B507/}.

quant-ph↗

arXiv2026

Lipschitz Dueling Bandits over Continuous Action Spaces

We study for the first time, stochastic dueling bandits over continuous action spaces with Lipschitz structure, where feedback is purely comparative. While dueling bandits and Lipschitz bandits have been studied separately, their combination has remained unexplored. We propose the first algorithm for Lipschitz dueling bandits, using round-based exploration and recursive region elimination guided by an adaptive reference arm. We develop new analytical tools for relative feedback and prove a regret bound of $\tilde O\left(T^{\frac{d_z+1}{d_z+2}}\right)$, where $d_z$ is the zooming dimension of the near-optimal region. Further, our algorithm takes only logarithmic space in terms of the total time horizon, best achievable by any bandit algorithm over a continuous action space.

cs.LG↗

arXiv2026

Distributionally Robust Listwise Preference Optimization

Existing robust preference optimization for language-model alignment mainly studies pairwise supervision and places robustness at the dataset, prompt, or preference-pair level. We instead study listwise preference optimization under ranking-label uncertainty: given a prompt and a candidate list, the observed ranking over that list may be ambiguous due to annotator inconsistency, near-ties, lossy rankwise feedback, or reward-model noise. We propose a pointwise total-variation robust Plackett--Luce objective that directly robustifies the ranking label conditional on the candidate list. The robust loss admits an exact decomposition into the nominal PL loss plus a worst-case PL correction, and the worst-case ranking is obtained by sorting current implicit scores in ascending order, reducing the inner maximization from $K!$ enumeration to $O(K\log K)$. This tractable structure yields strong offline and online optimization guarantees. In the offline fixed-list setting, the robust objective is convex and projected stochastic subgradient reaches global $ε$-suboptimality with $O(ε^{-2})$ sample complexity. In the online policy-induced setting, where candidate lists are generated by the current policy, we establish weak convexity and $\widetilde O(ε^{-2})$ Moreau-envelope stationarity. Experiments in offline LLM alignment show that the proposed robust correction largely preserves performance under clean labels and improves robustness under noise. In online alignment, it makes reward-model-ranked candidate expansion more reliable and improves both reward-model and external GPT-4 judge metrics.

cs.AI↗

arXiv2026

Learning Not to Optimize: Physics-Informed Action-Space Reshaping for Intent-Based Network Control

Modern network policy control maps intent to sequential placement-control decisions. Bellman-style policy optimization primarily asks which action to optimize, while constraints are commonly handled through penalty, barrier, or Lagrangian mechanisms. We observe that before a value function can certify the best deployment, intermediate signals may already identify many candidates that should be excluded from further optimization. This motivates a complementary direction: \emph{Learning Not to Optimize}. Before a value function is accurate enough to select the best placement-control decision, intermediate signals may already show that candidates are equivalent under state--intent relabeling (quotienting), lead to a uniformly worse future state (dominance), or violate executable network laws (residual screening). \LNOQRD{} uses these computed or learned signals as a shadow process to reshape the domain on which primal policy optimization is performed, thereby reducing the action space. We prove lossless quotienting and dominance under explicit equivariance and monotonicity conditions, bound frontier size and ranking cost, and quantify losses from approximate certificates and primal estimates. Experiments show that \LNOQRD{} reduces small-instance candidates by $75.9\%$ while retaining $90.8\%$ near-oracle coverage and, on large instances, achieves the highest utility and intent satisfaction, the lowest hard-law violation and post-generation latency, and a $73.0\%$ average reduction among candidate-based baselines.

cs.NI↗

arXiv2026

Hierarchical Multilevel Monte Carlo for Order-Optimal Neural Actor-Critic in Average-Reward CMDPs

Constrained Markov Decision Processes (CMDPs) provide a natural framework for reinforcement learning in safety-critical applications, where agents maximize long-term reward while satisfying long-term constraints. Although primal-dual actor-critic methods with linear critics are well understood, extending order-optimal convergence guarantees to neural critics in average-reward CMDPs has remained open. The main challenge is a fundamental bias-cost trade-off in neural critic estimation: under Neural Tangent Kernel (NTK) analysis, reducing critic bias substantially increases critic optimization cost, preventing order-optimal convergence in the primal-dual framework. We resolve this bottleneck by introducing a hierarchical Multilevel Monte Carlo (MLMC) neural critic that performs debiasing simultaneously across trajectory sampling and critic optimization. The resulting estimator attains the bias of a long critic optimization run with only logarithmic expected sample cost. Building on this estimator, we develop a primal-dual Natural Actor-Critic algorithm that achieves both an optimality gap and a constraint violation of order $\tilde{O}(T^{-1/2})$. This establishes the first order-optimal convergence guarantees for infinite-horizon average-reward CMDPs with general policy parameterization and neural critics, while eliminating the need to know the underlying mixing time. Our results are novel even in the unconstrained setting.

cs.LG↗

arXiv2026

Hypergradient-based Bilevel Reinforcement Learning with Improved Sample Complexity

Bilevel reinforcement learning (RL) is an important framework within the literature of RL that can be used to formalize various categories of problems, such as meta-learning, hierarchical task decomposition, and reinforcement learning from human feedback (RL-HF). Most of the bilevel RL algorithms are either not scalable because of using hypergradient with Hessian, or they suffer from high sample complexity because of using penalty-based approximation methods. In this work, we propose a hypergradient-based bilevel RL algorithm using the optimality of the Boltzmann policy for the entropy regularized discounted RL objective function. Our proposed algorithm is Hessian-free and obtains an iteration complexity of $O(ε^{-1})$ and state-of-the-art sample complexity of $\tilde{O}(ε^{-2})$ under mild regularity conditions. Further, in our convergence analysis, we are able to remove the assumption of the Polyak-Lojasiewicz (PL) condition on the outer-level objective function present in the prior state-of-the-art sample complexity work.

cs.LG↗

arXiv2026

Non-Expansive Two-Time-Scale Stochastic Approximation: A Fixed-Schedule One-Quarter Barrier and Bias-Corrected Acceleration

Non-expansive two-time-scale stochastic approximation is governed by a slow stochastic Krasnoselskii--Mann fixed-point iteration rather than by contraction to a unique equilibrium. We study this regime under a contractive fast map and a non-expansive reduced slow map. We first prove a finite-horizon lower bound showing that, for any prescribed slow stepsize schedule $(β_k)$, the classical KM residual scale $(\sum_{i<N}β_i(1-β_i))^{-1}$ is worst-case sharp for the corresponding unregularized KM update. Combined with the raw fast-tracking leakage scale, this explains the previously observed $k^{-1/4+o(1)}$ last-iterate mean-square residual exponent. We then introduce a residual-preconditioned slow oracle that cancels the first-order dependence on the fast tracking error. In a nested Tikhonov-KM algorithm, the uncorrected oracle yields total-sample rate $T^{-1/4+o(1)}$, while the corrected oracle yields $T^{-1/3+o(1)}$. This improvement comes from changing the slow-oracle bias from first order to second order in the fast error after all inner-loop samples are counted. Finally, we show that the repeated inner-loop cost of the nested method can be avoided in a smooth derivative-oracle model. A single-loop algorithm that tracks both the fast equilibrium and the leakage preconditioner online achieves $T^{-1/2+o(1)}$ with $O(1)$ primitive samples per iteration.

stat.ML↗

arXiv2026

Efficient Q-Learning and Actor-Critic Methods for Robust Average-Reward Reinforcement Learning

We study model-free methods for distributionally robust infinite-horizon average-reward Markov decision processes (MDPs). We present non-asymptotic convergence analyses of Q-learning and actor-critic algorithms for robust average-reward MDPs under contamination, total-variation distance, and Wasserstein uncertainty sets. A key ingredient of our analysis is showing that the optimal robust Bellman operator is a strict contraction with respect to a carefully designed semi-norm. This property enables a stochastic approximation update that learns the optimal robust $Q$-function with $\tilde{\mathcal{O}}(ε^{-2})$ dependence on the target accuracy. We also establish robust TD convergence bounds whose constants are uniform over all stationary policies, yielding an efficient data-driven routine for robust critic estimation. Building on this, we introduce an actor-critic algorithm that learns an $ε$-optimal robust policy with $\tilde{\mathcal{O}}(ε^{-2})$ dependence on the target accuracy. We provide numerical simulations to illustrate the qualitative behavior of the proposed algorithms. Our results contribute to the theoretical foundations of robust planning under model misspecification and to model-free approaches for building robust long-run policies directly from simulation data.

cs.LG↗

arXiv2026

Upper-Linearizability of Online Non-Monotone DR-Submodular Maximization over Down-Closed Convex Sets

We study online maximization of non-monotone Diminishing-Return(DR)-submodular functions over down-closed convex sets, a regime where existing projection-free online methods suffer from suboptimal regret and limited feedback guarantees. Our main contribution is a new structural result showing that this class is $1/e$-linearizable under carefully designed exponential reparametrization, scaling parameter, and surrogate potential, enabling a reduction to online linear optimization. As a result, we obtain $O(T^{1/2})$ static regret with a single gradient query per round and unlock adaptive and dynamic regret guarantees, together with improved rates under semi-bandit, bandit, and zeroth-order feedback. Across all feedback models, our bounds strictly improve the state of the art.

cs.LG↗

arXiv2026

A Technical Survey of Reinforcement Learning Techniques for Large Language Models

This survey offers a comprehensive foundation on the integration of RL with language models, highlighting prominent algorithms such as Proximal Policy Optimization (PPO), Q-Learning, and Actor-Critic methods. Additionally, it provides an extensive technical overview of RL techniques specifically tailored for LLMs, including foundational methods like Reinforcement Learning from Human Feedback (RLHF) and AI Feedback (RLAIF), as well as advanced strategies such as Direct Preference Optimization (DPO) and Group Relative Policy Optimization (GRPO). We systematically analyze their applications across domains, i.e., from code generation to tool-augmented reasoning. Crucially, we move beyond descriptive categorization to provide a rigorous algorithmic analysis of failure modes, mathematically framing the structural bottlenecks and stability trade-offs inherent in policy optimization. We also present a comparative taxonomy based on reward modeling, feedback mechanisms, and optimization strategies. Our evaluation highlights key trends. RLHF remains dominant for alignment, and outcome-based RL such as Reinforcement Learning with Verifiable Rewards (RLVR) significantly improves stepwise reasoning. However, persistent challenges such as reward hacking, computational costs, and scalable feedback collection underscore the need for continued innovation. We also explicate the causal factors behind recent benchmark performances, distinguishing between gains derived from architectural scaling versus those stemming from specific optimization objectives. We further discuss emerging directions, including hybrid RL algorithms, verifier-guided training, and multi-objective alignment frameworks. This survey serves as a roadmap for researchers advancing RL-driven LLM development, balancing capability enhancement with safety and scalability.

cs.AI↗

arXiv2026

On the Convergence of Self-Improving Online LLM Alignment

The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method. Empirically, SAIL has demonstrated strong performance on this task. However, a formal analysis of its convergence properties has been lacking. We identify a key theoretical challenge: the standard SAIL objective function is not guaranteed to be strongly concave due to unfavorable properties of its Hessian. To address this limitation, we propose a regularized objective, SAIL-RevKL, which incorporates a reverse Kullback-Leibler (KL) divergence penalty to improve the optimization landscape. Our central theoretical contribution is to prove that this regularized objective satisfies the Polyak-Lojasiewicz (PL) condition within a bounded parameter space. We establish global convergence guarantees, achieving a near-linear sample complexity. We further validate the effectiveness and stability of SAIL-RevKL through empirical evaluations, demonstrating that it outperforms the vanilla SAIL on both MuJoCo benchmarks and LLM alignment tasks.

cs.LG↗

arXiv2026

High-Probability PL-SGD with Markovian Noise: Optimal Mixing and Tail Dependence

We study first-order methods for smooth objectives satisfying the Polyak-Łojasiewicz (PL) condition when gradient samples are generated by an exogenous Markov chain. In the light-tailed setting, prior uniform-in-time high-probability bounds for ordinary Stochastic Gradient Descent (SGD) under a standard growth envelope scale as $\widetilde{O}(t_{mix}^2/k)$, leaving a gap with the $\widetilde{O}(t_{mix}/k)$ expectation bounds. We close this gap using a lag-blocking argument to establish a uniform high-probability guarantee with a leading stochastic term of $\widetilde{O}(t_{mix}/(k+K_0))$ under geometric mixing. We prove this linear dependence on the mixing time is optimal via a matching $Ω(σ^2 t_{mix}/k)$ lower bound on a quadratic objective driven by a persistent two-state chain. We then extend this framework to heavy-tailed Markovian gradients satisfying a stationary finite-$p$-moment condition, $p \in (1,2]$. We design an all-samples clipped block method that uses every Markov transition while mitigating Markovian bias. Under a transition budget $T$, this algorithm achieves a high-probability stochastic error of $\widetilde{O}(σ_p^2(t_{mix}/T)^{2(p-1)/p})$. We establish a matching lower bound by reducing PL optimization to heavy-tailed mean estimation for a sticky Markov chain. Ultimately, this work tightly characterizes the optimal polynomial dependence on mixing time for light-tailed PL-SGD, and the optimal heavy-tail exponent and effective-sample-size dependence in the robust regime.

cs.LG↗

arXiv2026

Bias-Controlled Primal-Dual Natural Actor-Critic: Optimal Rates for Constrained Multi-Objective Average-Reward RL

Many reinforcement learning (RL) problems in the infinite-horizon average-reward setting require optimizing multiple conflicting objectives while satisfying multiple safety constraints. A common approach is concave scalarization, where the agent maximizes a utility $ f(J^π_{r_1}, \ldots, J^π_{r_M}) $ subject to a scalarized constraint $ g(J^π_{c_1}, \ldots, J^π_{c_N}) \ge 0 $, where $J^π_{r_m}$ and $J^π_{c_n}$ denote the average-reward and cost under policy $π$. However, the nonlinearity of $f$ and $g$ introduces bias in policy-gradient and actor-critic methods, since gradients must be evaluated using noisy estimates of $J^π,$ and $ \mathbb{E}[\partial f(J^π)] \neq \partial f(\mathbb{E}[J^π]),$ and this bias propagates through both primal and dual updates. We propose an MLMC-based primal-dual Natural Actor-Critic algorithm for average-reward MDPs that controls bias in scalarized objectives, constraint evaluation, and actor-critic estimation without requiring mixing-time knowledge. We show that the algorithm achieves optimal global convergence and constraint-violation rates of $ \tilde{O}(1/\sqrt{T}) $. To our knowledge, this is the first result establishing optimal convergence for concave scalarized multi-objective RL in the average-reward setting, both with and without constraints, and the first to do so without mixing-time information even in the absence of scalarization.

cs.LG↗

arXiv2026

Discrete State Diffusion Models: A Sample Complexity Perspective

Diffusion models have demonstrated remarkable performance in generating high-dimensional samples across domains such as vision, language, and the sciences. Although continuous-state diffusion models have been extensively studied both empirically and theoretically, discrete-state diffusion models, essential for applications involving text, sequences, and combinatorial structures, remain significantly less understood from a theoretical standpoint. In particular, all existing analyses of discrete-state models assume score estimation error bounds without studying sample complexity results. In this work, we present a principled theoretical framework for discrete-state diffusion, providing the first sample complexity bound of $\widetilde{\mathcal{O}}(ε^{-2})$. Our structured decomposition of the score estimation error into statistical, approximation, optimization, and clipping components offers critical insights into how discrete-state models can be trained efficiently. This analysis addresses a fundamental gap in the literature and establishes the theoretical tractability and practical relevance of discrete-state diffusion models.

cs.LG↗

arXiv2026

Learning Policy from a Single Trajectory in Average-Reward Markov Decision Process

While there is an extensive body of work characterizing the sample complexity of discounted cumulative-reward MDPs, finite sample analyses for average-reward MDPs have been limited, and most existing works rely on restrictive assumptions such as ergodicity or access to a generative model. In this work, we establish the first finite sample complexity guarantees from a single trajectory for weakly communicating average-reward MDPs. To this end, we study the dynamics of a single trajectory in weakly communicating MDPs and based on this analysis, we develop novel model-free methods. Notably, our value-based and policy-based methods provide finite sample complexity guarantees of $\widetilde{O}(1/\varepsilon^2)$ and $\widetilde{O}(1/\varepsilon^4)$ from a single trajectory in weakly communicating MDPs, respectively. Furthermore, we introduce the first model-free method that requires no prior knowledge of problem-dependent quantities for communicating MDPs.

cs.LG↗

arXiv2026

Nonlinear Two-Time-Scale Stochastic Approximation: A Sharp Phase Transition and How to Beat It

Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $β_k=Θ(k^{-1})$ and $α_k=Θ(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity. We identify a sharp regularity-dependent boundary. In a rate-determining normal form where the slow drift contains a locally linear leakage and a nonlinear remainder of order $1+ρ$ ($ρ\in[0,1]$), the uncorrected recursion satisfies \[ \mathbb{E}\|Y_k\|^2 \le C\bigl(k^{-1}+k^{-a(1+ρ)}\bigr), \] and a matching scalar Gaussian lower bound shows that the slower term is unavoidable without modifying the update. Thus the decoupled $k^{-1}$ rate is guaranteed for the uncorrected recursion exactly when $a(1+ρ)\ge 1$. This lower bound concerns only the naive update; it is not an information-theoretic obstruction. We demonstrate this by equipping the normal-form recursion with an auxiliary online bias estimator \[ M_{k+1}=M_k+γ_k(R(X_k)-M_k),\qquad β_k\llγ_k\llα_k, \] and subtracting $M_k$ from the slow update. Under the same stability, moment, and remainder assumptions, the corrected recursion achieves $\mathbb{E}\|\widetilde Y_k\|^2=O(k^{-1})$ for every $ρ\in[0,1]$, including regimes where the uncorrected update provably suffers the slower rate. Finally, we prove localized transfer theorems that extend the phase-transition mechanism to general nonlinear TTSA in fast-manifold coordinates. The proofs are non-asymptotic and rely on two Abel-transform cancellations: one for the locally linear fast-error leakage, and one for the tracked nonlinear bias.

cs.IT↗