arXiv subjects

Vaneet Aggarwal

Publications and source records attributed to Vaneet Aggarwal.

At least 19 recordsLinked to original sources

arXiv2026

Constrained Online Learning with Noisy Constraint Values

We study constrained online convex optimization with adversarial constraints when constraint values and gradients are observed through unbiased noise. Gaussian value noise of standard deviation $\sigma$ yields a worst-case lower bound of $\Omega(\min\{\sigma,1\}T/\log^7T)$ on the maximum of expected regret and expected hard violation, even with known gradients. This rules out any jointly $O(T^{1-\delta})$ guarantee for fixed $\delta>0$ and fixed positive noise level. We therefore study budget violation: the largest cumulative overspend over any window within a fixed horizon. We introduce \LEDGER, which tracks observed net consumption in a nonnegative balance and sets constraint weights before the current feedback noise. Under common feasibility and conditional finite-variance feedback, for fixed problem parameters, \LEDGER\ achieves $O(\sqrt T/V)$ expected regret and $O(\sqrt V\,T^{3/4}+\sigma\sqrt T)$ expected budget violation for $V\in[T^{-1/2},1]$. This gives the pair $(O(\sqrt T),O(T^{3/4}))$ at $V=1$ and $(O(T^{2/3}),O(T^{2/3}))$ at $V=T^{-1/6}$, without a Slater condition. The budget-focused endpoint $V=T^{-1/2}$ gives $(O(T),O(\sqrt T))$. The same update yields $O((1+E[P_T])\sqrt T/V)$ expected dynamic regret for predictable feasible comparator paths, without common feasibility or path-length input. Its budget bound instead depends on the shortest feasible path, up to a dimension factor.

cs.LG↗

arXiv2026

Online Non-Monotone DR-Submodular Maximization Matching the Offline $0.401$ Factor

We study online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed subsets of the $d$-dimensional unit cube. The best known constructive offline approximation factor is $0.401$ under the corresponding meta-solvability assumptions, whereas comparable adversarial online guarantees had remained at $1/e$. We show that this factor is also achievable online. In the post-decision full-information value-oracle model, our algorithm attains factor $0.401$ with sublinear approximate regret when oracle feedback is conditionally unbiased and bounded. The online algorithm does not run the offline construction on a changing objective. Instead, it replaces the offline objective-dependent box step by a weighted online learner that controls the required residual terms cumulatively. An exact asymmetric balance theorem preserves the offline coefficients despite adversarial variation. The direct implementation has $O(T^{3/4})$ regret and uses $O(dT^{1/4})$ oracle calls per round. More generally, for every $\delta\in[0,1/4]$, batching gives $O(T^\delta)$ calls per round and $O(T^{4/5-\delta/5})$ regret, including a one-call $O(T^{4/5})$ endpoint. Under a positive-anchor condition, randomized blocking retains factor $0.401$ with $O(T^{5/6})$ one-point bandit regret.

cs.LG↗

arXiv2026

Dec-BFTRL: Squre-Root Regret for Decentralized Online Upper-Linearizable Optimization under Separation Access with Application to Continuous Submodular Maximization

We study decentralized online optimization of upper-linearizable payoffs over an action set under efficient separation access, with applications to online continuous diminishing-return (DR) submodular maximization. We propose Decentralized Barrier Follow-the-Regularized-Leader (Dec-BFTRL), and evaluate each agent's played action against the average of all local objectives. Each agent maps an internal iterate to a feasible action through an approximate gauge projection, communicates only a cumulative surrogate-gradient dual state, and invokes the local HybridNewton procedure to approximately minimize its post-communication BFTRL potential. For every agent, we achieve expected network-aggregate regret of $\widetilde O(\sqrt{T})$. Over $T$ rounds, each agent uses $T$ neighbor-mixing steps and $\widetilde O(T)$ separation-oracle calls. We give four wrapper instantiations covering three DR-submodular maximization problems.

math.OC↗

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 $\tau$-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

Sharp Minimax Regret for Infinite-Memory Logistic Prediction

We determine the minimax cumulative log-loss regret of a finite-alphabet, exogenously driven source with genuinely infinite input memory: independent Rademacher inputs $(U_t)$ are observed sequentially and the next binary mark has logit $\sum_{j\ge1}\theta_jU_{t+1-j}$, the unknown coefficients obeying a summable envelope $|\theta_j|\le r_j$, $\sum_jr_j\le B$. At horizon $T$, lag $j$ can move the logit by at most $r_j$ and is exercised in only $n_{T,j}=(T-j+1)_+$ rounds, and the two limitations combine into the sum $\Gamma_T(r)=\sum_{j\le T}\log(1+n_{T,j}r_j^{2})$. One coordinate-localised Bayesian mixture achieves $R_T(r)\le C\Gamma_T(r)$ for \emph{every} summable envelope with $C$ universal. Our main result is a matching nonasymptotic converse for the canonical exponential and polynomial envelopes; its new ingredients are a modular finite-sample information bound for logistic experiments with an exogenous random design, and a conditioning estimate for the overlapping Toeplitz lag matrix obtained by exhibiting each off-diagonal Gram sum as a sum of independent Rademacher variables indexed by the edges of a forest, needing neither local asymptotic normality nor any spectral theorem for random Toeplitz matrices. So $\Gamma_T(r)$ is the minimax regret scale here, giving $\Theta(\alpha^{-1}\log^{2}T)$ for $r_j=Ae^{-\alpha j}$ and $\Theta(T^{1/(2s)})$ for $r_j=Aj^{-s}$, $s>1$ --- the latter without the extra $(\log T)^{1-1/(2s)}$ factor any window-truncation analysis pays. We also show memory decay cannot determine regret, and that a profile-scaled online Newton predictor attains $O_B(\Gamma_T(r))$ in polynomial time per round.

cs.IT↗

arXiv2026

Online Convex Optimization with Dueling Feedback

We study online convex optimization with dueling (pairwise comparison) feedback, where the learner observes only a binary preference between two queried points. While dueling feedback is well understood in discrete or stochastic settings, the adversarial convex setting has remained unexplored. We propose a simple reduction that converts dueling feedback into approximate gradients, enabling the use of standard first-order methods. We show that regret guarantees transfer under this reduction, yielding the first results for this setting, including $\mathcal{O}(T^{3/4})$ static, adaptive, and dynamic regret. Under additional structure, we obtain improved rates of $\mathcal{O}(T^{2/3})$ for smooth objectives and $\mathcal{O}(\sqrt{T \log T})$ for strongly convex functions.

cs.LG↗

arXiv2026

Adversarial Resilience of Poisson-Process Submodular Maximization over Matroids, and Full-Bandit Learning

We study nonnegative submodular maximization on $n$ elements subject to a general matroid of rank $k$, when the offline algorithm is given an arbitrary controlled value oracle. Our main result is an adversarial resilience theorem for the Spiteful Greedy Swap Poisson Process (SGS-Poisson): without modifying its Poisson intensity, single-element exchange rule, or spiteful drop step, the algorithm retains limiting approximation factors $1/e$ for non-monotone objectives and $1-1/e$ for monotone objectives. More precisely, given an error bound $\xi\ge0$, under every controlled oracle $\widehat f$ satisfying $|\widehat f(S)-f(S)|\le \xi$ for every set $S$, our implementation returns a feasible set with expected value at least $(1/e-\varepsilon)OPT-O(k\xi)$ and $(1-1/e-\varepsilon)OPT-O(k\xi)$, respectively, where $OPT$ is the feasible optimum. The implementation uses a \emph{deterministically bounded} budget of $O(nk^{2}\varepsilon^{-2}\log n\log^{2}(1/\varepsilon))$ oracle calls. As a consequence, an offline-to-online reduction yields full-bandit combinatorial multi-armed bandit (CMAB) algorithms for general matroid-constrained submodular rewards with exact limiting approximation-regret factors $1/e$ and $1-1/e$ and $\widetilde O(n^{1/5}k^{4/5}T^{4/5})$ regret over $T$ rounds. These online guarantees allow exploration to play sets that become independent after deleting at most one element; exploitation and the benchmark remain matroid-feasible. For unit-capacity partition matroids we obtain $\widetilde O(n^{1/5}k^{3/5}T^{4/5})$ under the same exploration relaxation. We establish a deterministic query budget by truncating the Poisson process and identify the enlarged action set needed to answer its offline queries.

cs.LG↗

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 $O(\epsilon^{-1})$ and state-of-the-art sample complexity of $\tilde{O}(\epsilon^{-2})$ 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

Parameter-Free Dynamic Regret under Heavy-Tailed Noise

We study online convex optimization with stochastic gradient noise whose conditional $p$-th central moment is bounded by $\sigma^p$, for an unknown $p\in(1,2]$. For losses with Lipschitz bound $G$ on a domain of diameter $D$, we obtain expected universal dynamic regret $\widetilde O(GD\sqrt{T\Lambda}+\sigma DT^{1/p}\Lambda^{(p-1)/p})$, where $\Lambda=1+P_T/D$ and $P_T$ is the path length of a fixed comparator sequence. The algorithm combines restarted AdaGrad experts with an adaptive entropy-regularized master, uses one stochastic gradient per round, and requires no knowledge of $G,\sigma,p$, or $P_T$. Its iterates are invariant under positive rescaling of the gradients. The analysis controls comparator movement within restart blocks before taking expectations, yielding the noise path exponent $(p-1)/p$ rather than the exponent $1/2$ of a direct non-restarted extension. A matching stochastic first-order oracle lower bound, combined with the deterministic dynamic-regret lower bound, identifies the minimax rate up to logarithmic factors as $\min\{GD\sqrt{T\Lambda}+\sigma DT^{1/p}\Lambda^{(p-1)/p},GDT\}$.

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 $(\beta_k)$, the classical KM residual scale $(\sum_{i<N}\beta_i(1-\beta_i))^{-1}$ 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

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 $\epsilon$-suboptimality with $O(\epsilon^{-2})$ sample complexity. In the online policy-induced setting, where candidate lists are generated by the current policy, we establish weak convexity and $\widetilde O(\epsilon^{-2})$ 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

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-\L{}ojasiewicz (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 $\Omega(\sigma^2 t_{mix}/k)$ 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 $\widetilde{O}(\sigma_p^2(t_{mix}/T)^{2(p-1)/p})$. 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^\pi_{r_1}, \ldots, J^\pi_{r_M}) $ subject to a scalarized constraint $ g(J^\pi_{c_1}, \ldots, J^\pi_{c_N}) \ge 0 $, where $J^\pi_{r_m}$ and $J^\pi_{c_n}$ denote the average-reward and cost under policy $\pi$. 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 $J^\pi,$ and $ \mathbb{E}[\partial f(J^\pi)] \neq \partial f(\mathbb{E}[J^\pi]),$ 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

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 $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, 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 $1+\rho$ ($\rho\in[0,1]$), the uncorrected recursion satisfies \[ \mathbb{E}\|Y_k\|^2 \le C\bigl(k^{-1}+k^{-a(1+\rho)}\bigr), \] 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 $a(1+\rho)\ge 1$. 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 \[ M_{k+1}=M_k+\gamma_k(R(X_k)-M_k),\qquad \beta_k\ll\gamma_k\ll\alpha_k, \] 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 $\rho\in[0,1]$, 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↗