arXiv subjects

Vartika Singh

Publications and source records attributed to Vartika Singh.

18 recordsLinked to original sources

arXiv2026

Truncated Noisy Best-Response Algorithms: Toward Game Theoretic Learning with Safety Guarantees

We consider a game theoretic approach to solve multi-agent coordination problems with submodular maximization objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal, but that the equilibria which achieve this worst-case bound are not stable. To exploit this instability, we propose a family of algorithms which we call Truncated Noisy Best-Response (TNBR) Algorithms. These algorithms are flexibly characterized by agents asynchronously and stochastically selecting actions from a neighbourhood of their best response payoffs. We compute bounds on the recurrent classes of TNBR algorithms' associated Markov chains. Our bounds fall into two categories: first, "Performance" bounds ensure that TNBR algorithms always have a high-value recurrent state; second, "Safety" bounds ensure that TNBR algorithms never have arbitrarily-bad recurrent states. Furthermore, these two types of bounds are linked by a waterbed-like effect: every game with a poor Safety guarantee necessarily has a favorable Performance guarantee.

cs.GT↗

arXiv2026

Deriving the Pure Price of Anarchy for Networked Resource Allocation Games

This work considers multi-agent coordination with arbitrary information networks among the agents using a game-theoretic approach. A system designer aims to assign local utility functions to the agents to guide their actions toward a desired system objective. The performance of the assigned local utilities is measured by the well known pure price of anarchy (pPoA) metric that equals the ratio of the system objective at the worst pure Nash equilibrium of the corresponding game to the optimal system objective. Our aim is to derive the utility functions which optimize the pPoA-based performance guarantees for any given information network and system objective. We develop a linear program that derives the optimal pPoA for any arbitrary information network and arbitrary system objective. Our work is the first to solve optimal utility design for arbitrary networks; our techniques generalize previous approaches which considered only the full-information setting. For supermodular objective functions, we prove that counterintuitively, a fully communication-denied utility design is optimal irrespective of the original information network. For submodular system objectives, an exhaustive numerical analysis suggests that the optimal utility design is robust to communication failures even for this case. When the system objective is weighted maximum coverage, the marginal contribution utility design provably optimizes the pPoA for a wide variety of information networks of interest.

cs.GT↗

arXiv2026

ABRA: An algorithm which cannot converge to low-quality Nash equilibria

We consider a game theoretic approach to solve multi-agent coordination problems with submodular objectives. It is known for such problems that the Nash equilibria for the corresponding game are always within 50% of the optimal. A recent work further shows that the equilibria which achieve this worst-case bound are not stable. Leveraging this, we design an Approximate Best Response Algorithm (ABRA) governed by a noise parameter and a rationality parameter. The noise allows ABRA to escape the bad equilibria and the rationality parameter balances any degradation in the objective function caused by the noise. We show for any two-player game that if ABRA converges to a Nash equilibrium, its system objective value is strictly more than 50% of optimal plus a term controlled by the noise parameter. Otherwise, ABRA converges to some recurrent class: if a recurrent class contains any action profile yielding system objective less than 50% of the optimal, the class must also contain either the optimal action profile or an action profile yielding system objective strictly more than 50\% of the optimal by the same amount in addition to a factor controlled by noise parameter. The time that ABRA spends in such action profiles can be controlled using the rationality parameter. Using numerical simulations, we show that the minimum expected objective function is typically well above half of the optimal.

cs.GT↗

arXiv2026

Hadronic tau decays at higher orders in QCD

We investigate higher-order perturbative corrections to hadronic $τ$ decays by applying nonlinear sequence-transformation techniques to the QCD correction $δ^{(0)}$. In particular, we employ the Shanks transformation and several of its generalisations constructed through Wynn's $\varepsilon$-algorithm, which are known to accelerate the convergence of slowly convergent or divergent series. These methods are used to extract higher-order information from the fixed-order perturbative expansion of $δ^{(0)}$. Within this framework, we estimate the perturbative coefficients $c_{5,1}$-$c_{12,1}$. In particular, we obtain $c_{5,1}=298 \pm 15$, $c_{6,1}=3431 \pm 256$, and $c_{7,1}=2.29 \pm 0.29\times 10^4$, where the quoted uncertainties reflect the spread among the different sequence transformations employed. Moreover, we predict the QCD correction $ δ^{(0) }_{\text{FOPT}}=0.2119 \pm 0.0040\pm 0.0065_{α_s} $. Our analysis demonstrates that non-linear sequence transformations, such as the Shanks-type, provide an efficient and systematic tool for probing higher-order perturbative effects in hadronic $τ$ decays in the absence of explicit multi-loop calculations.

hep-ph↗

arXiv2026

SOL-ExecBench: Speed-of-Light Benchmarking for Real-World GPU Kernels Against Hardware Limits

As agentic AI systems become increasingly capable of generating and optimizing GPU kernels, progress is constrained by benchmarks that reward speedup over software baselines rather than proximity to hardware-efficient execution. We present SOL-ExecBench, a benchmark of 235 CUDA kernel optimization problems extracted from 124 production and emerging AI models spanning language, diffusion, vision, audio, video, and hybrid architectures, targeting NVIDIA Blackwell GPUs. The benchmark covers forward and backward workloads across BF16, FP8, and NVFP4, including kernels whose best performance is expected to rely on Blackwell-specific capabilities. Unlike prior benchmarks that evaluate kernels primarily relative to software implementations, SOL-ExecBench measures performance against analytically derived Speed-of-Light (SOL) bounds computed by SOLAR, our pipeline for deriving hardware-grounded SOL bounds, yielding a fixed target for hardware-efficient optimization. We report a SOL Score that quantifies how much of the gap between a release-defined scoring baseline and the hardware SOL bound a candidate kernel closes. To support robust evaluation of agentic optimizers, we additionally provide a sandboxed harness with GPU clock locking, L2 cache clearing, isolated subprocess execution, and static analysis based checks against common reward-hacking strategies. SOL-ExecBench reframes GPU kernel benchmarking from beating a mutable software baseline to closing the remaining gap to hardware Speed-of-Light.

cs.LG↗

arXiv2026

Dark-technicolour at colliders

We demonstrate that QCD-like gauge dynamics can be consistently embedded within the Dark Technicolor paradigm by invoking the extended Most Attractive Channel hypothesis, thereby revitalizing conventional technicolor scenarios. In this framework, the Higgs mass is generated dynamically while remaining consistent with electroweak precision tests, including constraints from the $S$ parameter. The flavor problem is resolved by incorporating the Standard Hierarchical VEVs Model, whereas a simple Froggatt--Nielsen construction is shown to be incompatible. Couplings of techni-hadrons such as $ρ_{\rm TC}$ and $η_{\rm TC}^\prime$ to Standard Model fermions are highly suppressed, leading to negligible direct fermionic signatures. Nevertheless, DTC mesons remain testable at the HL-LHC, HE-LHC, and future 100~TeV collider, with promising discovery channels including $\bar{b}b$, $τ^+τ^-$, $t\bar{t}$, and $γγ$.

hep-ph↗

arXiv2026

A new determination of higher-order QCD corrections to hadronic $τ$ decays

We employ \textit{Levin-type sequence transformations} to accelerate the convergence of the perturbative fixed-order expansion of the QCD correction $δ^{(0)}$ in terms of the strong coupling $α_s$. The method efficiently resums the series, yielding a stable and self-consistent determination of higher-order QCD corrections to hadronic $τ$ decays, consistent with existing results. We find $δ^{(0)}_{\text{Levin-FOPT}} = 0.2089 \pm 0.0040 \, \pm 0.0060_{α_s} \, $, and predict $ c_{5,1} = 278^{+27}_{-19}, \quad c_{6,1} = 3375^{+489}_{-209}, \quad c_{7,1} = (2.03^{+0.41}_{-0.25}) \times 10^4. $ Our results demonstrate that Levin-type transformations provide an efficient framework for analyzing asymptotic perturbative series, and studying the higher order perturbative behaviour of the hadronic $τ$ decays.

hep-ph↗

arXiv2025

TiDAR: Think in Diffusion, Talk in Autoregression

Diffusion language models hold the promise of fast parallel generation, while autoregressive (AR) models typically excel in quality due to their causal structure aligning naturally with language modeling. This raises a fundamental question: can we achieve a synergy with high throughput, higher GPU utilization, and AR level quality? Existing methods fail to effectively balance these two aspects, either prioritizing AR using a weaker model for sequential drafting (speculative decoding), leading to lower drafting efficiency, or using some form of left-to-right (AR-like) decoding logic for diffusion, which still suffers from quality degradation and forfeits its potential parallelizability. We introduce TiDAR, a sequence-level hybrid architecture that drafts tokens (Thinking) in Diffusion and samples final outputs (Talking) AutoRegressively - all within a single forward pass using specially designed structured attention masks. This design exploits the free GPU compute density, achieving a strong balance between drafting and verification capacity. Moreover, TiDAR is designed to be serving-friendly (low overhead) as a standalone model. We extensively evaluate TiDAR against AR models, speculative decoding, and diffusion variants across generative and likelihood tasks at 1.5B and 8B scales. Thanks to the parallel drafting and sampling as well as exact KV cache support, TiDAR outperforms speculative decoding in measured throughput and surpasses diffusion models like Dream and Llada in both efficiency and quality. Most notably, TiDAR is the first architecture to close the quality gap with AR models while delivering 4.71x to 5.91x more tokens per second.

cs.CL↗

arXiv2025

Stability of Polling Systems for a Large Class of Markovian Switching Policies

We consider a polling system with two queues, where a single server is attending the queues in a cyclic order and requires non-zero switching times to switch between the queues. Our aim is to identify a fairly general and comprehensive class of Markovian switching policies that renders the system stable. Potentially a class of policies that can cover the Pareto frontier related to individual-queue-centric performance measures like the stationary expected number of waiting customers in each queue; for instance, such a class of policies is identified recently for a polling system near the fluid regime (with large arrival and departure rates), and we aim to include that class. We also aim to include a second class that facilitates switching between the queues at the instance the occupancy in the opposite queue crosses a threshold and when that in the visiting queue is below a threshold (this inclusion facilitates design of `robust' polling systems). Towards this, we consider a class of two-phase switching policies, which includes the above mentioned classes. In the maximum generality, our policies can be represented by eight parameters, while two parameters are sufficient to represent the aforementioned classes. We provide simple conditions to identify the sub-class of switching policies that ensure system stability. By numerically tuning the parameters of the proposed class, we illustrate that the proposed class can cover the Pareto frontier for the stationary expected number of customers in the two queues.

math.OC↗

arXiv2025

Optimal Utility Design with Arbitrary Information Networks

We consider multi-agent systems with general information networks where an agent may only observe a subset of other agents. A system designer assigns local utility functions to the agents guiding their actions towards an outcome which determines the value of a given system objective. The aim is to design these local utility functions such that the Price of Anarchy (PoA), which equals the ratio of system objective at worst possible outcome to that at the optimal, is maximized. Towards this, we first develop a linear program (LP) that characterizes the PoA for any utility design and any information network. This leads to another LP that optimizes the PoA and derives the optimal utility design. Our work substantially generalizes existing approaches to the utility design problem. We also numerically show the robustness of proposed framework against unanticipated communication failures.

cs.GT↗

arXiv2024

An Empirical Study of Mamba-based Language Models

Selective state-space models (SSMs) like Mamba overcome some of the shortcomings of Transformers, such as quadratic computational complexity with sequence length and large inference-time memory requirements from the key-value cache. Moreover, recent studies have shown that SSMs can match or exceed the language modeling capabilities of Transformers, making them an attractive alternative. In a controlled setting (e.g., same data), however, studies so far have only presented small scale experiments comparing SSMs to Transformers. To understand the strengths and weaknesses of these architectures at larger scales, we present a direct comparison between 8B-parameter Mamba, Mamba-2, and Transformer models trained on the same datasets of up to 3.5T tokens. We also compare these models to a hybrid architecture consisting of 43% Mamba-2, 7% attention, and 50% MLP layers (Mamba-2-Hybrid). Using a diverse set of tasks, we answer the question of whether Mamba models can match Transformers at larger training budgets. Our results show that while pure SSMs match or exceed Transformers on many tasks, they lag behind Transformers on tasks which require strong copying or in-context learning abilities (e.g., 5-shot MMLU, Phonebook) or long-context reasoning. In contrast, we find that the 8B Mamba-2-Hybrid exceeds the 8B Transformer on all 12 standard tasks we evaluated (+2.65 points on average) and is predicted to be up to 8x faster when generating tokens at inference time. To validate long-context capabilities, we provide additional experiments evaluating variants of the Mamba-2-Hybrid and Transformer extended to support 16K, 32K, and 128K sequences. On an additional 23 long-context tasks, the hybrid model continues to closely match or exceed the Transformer on average. To enable further study, we release the checkpoints as well as the code used to train our models as part of NVIDIA's Megatron-LM project.

cs.LG↗

arXiv2024

Renormalization-group improved Higgs to two gluons decay rate

We investigate the renormalization-group scale and scheme dependence of the $H \rightarrow gg$ decay rate at the order N$^4$LO in the renormalization-group summed perturbative theory, which employs the summation of all renormalization-group accessible logarithms including the leading and subsequent four sub-leading logarithmic contributions to the full perturbative series expansion. Moreover, we study the higher-order behaviour of the $H \rightarrow gg$ decay width using the asymptotic Padé approximant method in four different renormalization schemes. Furthermore, the higher-order behaviour is independently investigated in the framework of the asymptotic Padé-Borel approximant method where generalized Borel-transform is used as an analytic continuation of the original perturbative expansion. The predictions of the asymptotic Padé-Borel approximant method are found to be in agreement with that of the asymptotic Padé approximant method. Finally, we provide the $H \rightarrow gg$ decay rate at the order N$^5$LO in the fixed-order $ Γ_{\rm N^5LO} \,=\, Γ_0 (1.8375 \pm 0.047 _{α_s(M_Z),1\%}\pm 0.0004_{M_t} \pm 0.0066_{M_H} \pm 0.0036_{\rm P} \pm 0.007_{\text{s}} \pm 0.0005_{sc} ),$ and $Γ_{\rm RGSN^5LO} \,=\, Γ_0 (1.841 \pm 0.047 _{α_s(M_Z),1\%} \pm 0.0005_{M_t}\pm 0.0066_{M_H} \pm 0.0002_μ \pm 0.0027_{\rm P} \pm 0.001_{sc} )$ in the renormalization-group summed perturbative theories.

hep-ph↗

arXiv2023

Stochastic vaccination game among influencers, leader and public

Celebrities can significantly influence the public towards any desired outcome. In a bid to tackle an infectious disease, a leader (government) exploits such influence towards motivating a fraction of public to get vaccinated, sufficient enough to ensure eradication. The leader also aims to minimize the vaccinated fraction of public (that ensures eradication) and use minimal incentives to motivate the influencers; it also controls vaccine-supply-rates. Towards this, we consider a three-layered Stackelberg game, with the leader at the top. A set of influencers at the middle layer are involved in a stochastic vaccination game driven by incentives. The public at the bottom layer is involved in an evolutionary game with respect to vaccine responses. We prove the disease can always be eradicated once the public is sufficiently sensitive towards the vaccination choices of the influencers -- with a minimal fraction of public vaccinated. This minimal fraction depends only on the disease characteristics and not on other aspects. Interestingly, there are many configurations to achieve eradication, each configuration is specified by a dynamic vaccine-supply-rate and a number -- this number represents the count of the influencers that needs to be vaccinated to achieve the desired influence. Incentive schemes are optimal when this number equals all or just one; the former curbs free-riding among influencers while the latter minimizes the dependency on influencers.

math.OC↗

arXiv2023

Flavour bounds on the flavon of a minimal and a non-minimal $\mathcal{Z}_2 \times \mathcal{Z}_N$ symmetry

We investigate flavour bounds on the $\mathcal{Z}_2 \times \mathcal{Z}_5$ and $\mathcal{Z}_2 \times \mathcal{Z}_9$ flavour symmetries. These flavour symmetries are a minimal and a non-minimal forms of the $\mathcal{Z}_2 \times \mathcal{Z}_N$ flavour symmetry, that can provide a simple set-up for the Froggatt-Nielsen mechanism. The $\mathcal{Z}_2 \times \mathcal{Z}_5$ and $\mathcal{Z}_2 \times \mathcal{Z}_9$ flavour symmetries are capable of explaining the fermionic masses and mixing pattern of the standard model including that of the neutrinos. The bounds on the parameter space of the flavon field of the $\mathcal{Z}_2 \times \mathcal{Z}_5$ and $\mathcal{Z}_2 \times \mathcal{Z}_9$ flavour symmetries are derived using the current quark and lepton flavour physics data and future projected sensitivities of quark and lepton flavour effects. The strongest bounds on the flavon of the $\mathcal{Z}_2 \times \mathcal{Z}_5$ symmetry come from the $D^0 - \bar D^0$ mixing. The bounds on the $\mathcal{Z}_2 \times \mathcal{Z}_9$ flavour symmetry are stronger than that of the minimal $\mathcal{Z}_2 \times \mathcal{Z}_5$ symmetry. The ratio $R_{μμ}$ provides rather robust bounds on the flavon parameters in the future phase-\rom{1} and phase-\rom{2} of the LHCb by leaving only a very small region in the allowed parameter space of the models.

hep-ph↗

arXiv2023

Fixed-point equations solving Risk-sensitive MDP with constraint

There are no computationally feasible algorithms that provide solutions to the finite horizon Risk-sensitive Constrained Markov Decision Process (Risk-CMDP) problem, even for problems with moderate horizon. With an aim to design the same, we derive a fixed-point equation such that the optimal policy of Risk-CMDP is also a solution. We further provide two optimization problems equivalent to the Risk-CMDP. These formulations are instrumental in designing a global algorithm that converges to the optimal policy. The proposed algorithm is based on random restarts and a local improvement step, where the local improvement step utilizes the solution of the derived fixed-point equation; random restarts ensure global optimization. We also provide numerical examples to illustrate the feasibility of our algorithm for inventory control problem with risk-sensitive cost and constraint. The complexity of the algorithm grows only linearly with the time-horizon.

math.OC↗

arXiv2022

Fair opportunistic schedulers for Lossy Polling systems

Polling systems with losses are useful mathematical objects that can model many practical systems like travelling salesman problem with recurrent requests. One of the less studied yet an important aspect in such systems is the disparity in the utilities derived by the individual stations. Further, the random fluctuations of the travel conditions can have significant impact on the performance. This calls for a scheduler that caters to the fairness aspect, depends upon the travel conditions and the dynamic system state. Inspired by the generalized alpha-fair schedulers of wireless networks, we propose a family of schedulers that further considers binary knowledge of the travel conditions. These schedulers are opportunistic, allocate the server to a station with bad travel condition only when the station has accumulated too little a utility by the decision epoch. We illustrate that the disparities among the individual utilities diminish to zero, as fairness factor increases, and further that the price of fairness decreases as the number of stations increase.

math.OC↗

arXiv2021

Evolutionary Vaccination Games with premature vaccines to combat ongoing deadly pandemic

We consider a vaccination game that results with the introduction of premature and possibly scarce vaccines introduced in a desperate bid to combat the otherwise ravaging deadly pandemic. The response of unsure agents amid many uncertainties makes this game completely different from the previous studies. We construct a framework that combines SIS epidemic model with a variety of dynamic behavioral vaccination responses and demographic aspects. The response of each agent is influenced by the vaccination hesitancy and urgency, which arise due to their personal belief about efficacy and side-effects of the vaccine, disease characteristics, and relevant reported information (e.g., side-effects, disease statistics etc.). Based on such aspects, we identify the responses that are stable against static mutations. By analysing the attractors of the resulting ODEs, we observe interesting patterns in the limiting state of the system under evolutionary stable (ES) strategies, as a function of various defining parameters. There are responses for which the disease is eradicated completely (at limiting state), but none are stable against mutations. Also, vaccination abundance results in higher infected fractions at ES limiting state, irrespective of the disease death rate.

math.DS↗

arXiv2020

Asymmetric Information Acquisition Games

We consider a stochastic game with partial, asymmetric and non-classical information, where the agents are trying to acquire as many available opportunities/locks as possible. Agents have access only to local information, the information updates are asynchronous and our aim is to obtain relevant equilibrium policies. Our approach is to consider optimal open-loop control until the information update, which allows managing the belief updates in a structured manner. The agents continuously control the rates of their Poisson search clocks to acquire the locks, and they get rewards at every successful acquisition; an acquisition is successful if all the previous stages are successful and if the agent is the first one to complete. However, none of them have access to the acquisition status of the other agents, leading to an asymmetric information game. Using standard tools of optimal control theory and Markov decision process (MDP) we solved a bi-level control problem; every stage of the dynamic programming equation of the MDP is solved using optimal control tools. We finally reduced the game with an infinite number of states and infinite-dimensional actions to a finite state game with one-dimensional actions. We provided closed-form expressions for Nash Equilibrium in some special cases and derived asymptotic expressions for some more.

math.OC↗