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Shravan Mohan

Publications and source records attributed to Shravan Mohan.

16 recordsLinked to original sources

GRPO for Financial Advice Generation: Outperforming Commercial LLMs under CATE Evaluation

Generating actionable financial advice from business records demands that models integrate numerical reasoning, domain knowledge, and sound judgment, while avoiding recommendations that could harm the business. Direct supervision is difficult: historical decisions are not necessarily optimal, and high-quality free-form labels are expensive to obtain. We formulate financial advice generation as a reinforcement learning problem and fine-tune an open-weight language model using Group Relative Policy Optimization (GRPO). Our reward is an LLM-as-a-judge rubric that scores each recommendation across multiple binary dimensions of advice quality, augmented with a safety gate for harm prevention. Since LLM-based evaluation alone cannot confirm whether improvements reflect genuine business value rather than adaptation to the judge, we complement it with a judge-independent audit based on a standard doubly-robust Conditional Average Treatment Effect (CATE) estimator. Under this observational off-policy audit, our trained LLM achieves approximately twice the estimated gross-profit lift of the strongest evaluated commercial baseline ($0.0228$ vs.\ $0.0104$), together with the lowest downside rate and the least negative tail risk of any policy evaluated. Notably, the two evaluations do not rank the baselines identically: the untrained base model places last on the judge rubric but second on the causal audit, indicating that the audit captures a signal the judge does not. Our results demonstrate that GRPO with a finance-grounded reward signal can produce substantially more useful business recommendations than commercial LLMs, and that a judge-independent causal audit is a valuable complement to, rather than a confirmation of, LLM-as-a-judge assessment in financial NLP.

cs.CL

On feasibility problems with spectral constraints

We study matrix feasibility problems "find X in K intersect C" where K is a closed convex matrix set and C = {X : sigma(X) in S} is defined by a convex constraint S on the ordered singular values. Using the classical spectral transfer identity, projection onto C reduces to an SVD plus a small quadratic program. For seven natural polyhedral S we embed this projector in a plain alternating projection (AP) loop. We experiment with two concrete families of K - linear constraints (an affine subspace intersected with an entrywise box) and ellipsoidal constraints (a non-centered anisotropic Frobenius ellipsoid) - although the method applies equally to more general convex constraints. The experiments expose three regimes: rapid feasibility, slow tail convergence, or informative infeasibility plateaus.

math.OC

On a group of invariances in a class of functions

A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this family, nontrivial parametric invariances are identified and characterized, i.e., distinct parameter settings that induce identical input-output maps. A constructive description of the invariance structure is provided, enabling sparse function representations, parameter obfuscation, and potential dimensionality reduction for optimization.

math.OC

A note on finding optimal cut-offs

This paper addresses the challenge of determining optimal cut-offs for a set of n items with m scores to maximize distinguishability. The term distinguishability is defined as the fraction of item pairs assigned to different buckets, where buckets are determined by the number of cut-offs an items scores exceed. A brute-force approach to this problem is computationally intractable, with complexity growing exponentially with the number of scores. On the other hand, attempts to solve the problem in the continuous domain lead to local minima, making it unreliable. To overcome these challenges, the problem is formulated as a Integer Quadratic Program (IQP). Since IQPs become computationally difficult with even moderate size problems, a surrogate Integer Linear Program (ILP) is introduced, which can be solved more efficiently for larger instances. In addition to these exact methods, a simple heuristic is proposed that offers a balance between solution quality and computational efficiency. This heuristic iteratively adjusts cutoffs for each score, considering a finite-set of meaningful cut-off points. Computational results provide an empirically evidence for the effectiveness of our proposed methods.

math.OC

A conjecture related to the Newman phase

A conjecture is proposed concerning the recovery of a discrete magnitude spectrum through a nonlinear transformation involving the Newman's phase sequence. Given a discrete magnitude spectrum sampled from a continuous function, consider the process of applying a complex exponential with the Newman's phase sequence, computing the inverse discrete Fourier transform (IFFT), taking the absolute value of the result, and reversing the time-domain signal. The conjecture states that Newman's phase sequence, defined by a formula $\phi^{(N)}[k] = \frac{\pi (k-1)^2}{N}$, asymptotically recovers the original magnitude spectrum as the number of samples $N \to \infty$. Notably, the phase sequence is also independent of the input signal and is unique up to an overall constant phase shift. The broader implications of this conjecture remain to be fully understood, but the phenomenon raises fundamental questions about the role of phase in nonlinear spectral recovery.

math.OC

A parallelizable variant of HCA*

This paper presents a parallelizable variant of the well-known Hierarchical Cooperative A* algorithm (HCA*) for the multi-agent path finding (MAPF) problem. In this variant, all agents initially find their shortest paths disregarding the presence of others. This is done using A*. Then an intersection graph (IG) is constructed; each agent is a node and two nodes have an edge between them if the paths of corresponding agents collide. Thereafter, an independent set is extracted with the aid of an approximation algorithm for the maximum independent set problem. The paths for the agents belonging to independent set are fixed. The rest of agents now again find their shortest paths, this time ensuring no collision with the prior agents. Space-time A*, which is a crucial component of HCA*, is used here. These iterations continue until no agents are left. Since the tasks of finding shortest paths for the agents in any iteration are independent of each other, the proposed algorithm can be parallelized to a large extent. In addition to this, the task of determining the IG can also be done in parallel by dividing the map into sections and with each agent focusing on a particular section. The parallelism does come at a cost of communication between the agents and the server. This is accounted for in the simulations. As an added advantage, the user need not make a choice for the priority order. It is observed, empirically, that the proposed algorithm outperforms HCA* in terms of the computation time and the cost value in many cases. Simulations are provided for corroboration.

eess.SY

On extending the class of convex functions

In this brief note, it is shown that the function p^TW log(p) is convex in p if W is a diagonally dominant positive definite M-matrix. The techniques used to prove convexity are well-known in linear algebra and essentially involves factoring the Hessian in a way that is amenable to martix analysis. Using similar techniques, two classes of convex homogeneous polynomials is derived - namely, p^TW p2 and (p^k)^TW p^k - the latter also happen to be SOS-convex. Lastly, usign the same techniques, it is also shown that the function p^TW ep is convex over the positive reals only if W is a non-negative diagonal matrix. Discussions regarding the utility of these functions and examples accompany the results presented.

math.OC

A note on the Bures-Wasserstein metric

In this brief note, it is shown that the Bures-Wasserstein (BW) metric on the space positive definite matrices lends itself to convex optimization. In other words, the computation of the BW metric can be posed as a convex optimization problem. In turn, this leads to efficient computations of (i) the BW distance between convex subsets of positive definite matrices, (ii) the BW barycenter, and (iii) incorporating BW distance from a given matrix as a convex constraint. Computations are provided for corroboration.

math.OC

A note on power allocation for optimal capacity

The problems of determining the optimal power allocation, within maximum power bounds, to (i) maximize the minimum Shannon capacity, and (ii) minimize the weighted latency are considered. In the first case, the global optima can be achieved in polynomial time by solving a sequence of linear programs (LP). In the second case, the original non-convex problem is replaced by a convex surrogate (a geometric program), using a functional approximation. Since the approximation error is relatively low, the optima of the surrogate is close to the global optimal point of the original problem. In either cases, there is no assumption on the SINR range. The use of LPs and geometric programming make the proposed algorithms numerically efficient. Computations are provided for corroboration.

eess.SY

A note on load balancing in DC microgrids

A problem of load balancing in isolated DC microgrids is considered in this paper. Here, a DC load is fed by multiple heterogenous DC sources, each of which is connected to the load via a boost converter. The gains of the DCC's provide for a means to control the division of load current amongst the DC sources. The primary objective of the control scheme is to minimise the total losses in the network, while maintaining the output voltage within a desired range, serving the load current demand and adhering to VI-characteristics of the power sources. Under assumptions of concavity/monotonocity/piece-wise-linearity of the VI-characteristics, the problem is solved using a convex relaxation. It is shown that the solution to the relaxed problem is tight. Thus, the resulting algorithm is guaranteed to reach global optimality in a numerically efficient manner. Simulations are provided for corroboration.

eess.SY

Optimal Switching of Controlled Rectifiers

This paper discusses a linear programming approach for designing switching signals for controlled rectifiers to achieve a low input current & output voltage total harmonic distortions. The focus here is on fully controlled rectifiers made with four-quadrant MOSFET based switches. This topology, unlike thyristor based rectifiers, can be turned ON or OFF anytime. Yet another assumption made here is that the current drawn by the load is constant. The basic idea for designing the waveform is to first time discretize its one period. This discretization, along with Parsevals identity lead to a linear programming formulation for minimizing a weighted sum of total harmonic distortions of the input current and the output voltages. The LPs so obtained can be solved efficiently using standard solvers to obtain the switching instants. The method can be used for both single phase and three-phase rectifiers. Simulations are provided for corroboration.

eess.SY

Control of Permanent Magnet Motors with Actuation Bounds using Convex Optimization

This paper presents a nonlinear control algorithm for speed control of a permanent magnet motor. The idea relies on a feedback linearization technique which also ensures adherence to current and voltage bounds. These bounds arise from practical limitations of the power source. The feedback linearization law is computed using a convex optimization routine to minimize response time as well. The aid of convex optimization leads to computational efficiency. Moreover, the mathematical tractability of the approach also aids analysis of the system performance under model uncertainty and feedback measurement noise. Simulations and computations corroborate the proposed idea.

eess.SY

A note on rank constrained solutions to linear matrix equations

This preliminary note presents a heuristic for determining rank constrained solutions to linear matrix equations (LME). The method proposed here is based on minimizing a non-convex quadratic functional, which will hence-forth be termed as the \textit{Low-Rank-Functional} (LRF). Although this method lacks a formal proof/comprehensive analysis, for example in terms of a probabilistic guarantee for converging to a solution, the proposed idea is intuitive and has been seen to perform well in simulations. To that end, many numerical examples are provided to corroborate the idea.

math.OC

On the primal-dual dynamics of Support Vector Machines

The aim of this paper is to study the convergence of the primal-dual dynamics pertaining to Support Vector Machines (SVM). The optimization routine, used for determining an SVM for classification, is first formulated as a dynamical system. The dynamical system is constructed such that its equilibrium point is the solution to the SVM optimization problem. It is then shown, using passivity theory, that the dynamical system is global asymptotically stable. In other words, the dynamical system converges onto the optimal solution asymptotically, irrespective of the initial condition. Simulations and computations are provided for corroboration.

eess.SY

A linear programming approach for designing multilevel PWM waveforms

This paper considers the problem of designing a multilevel pulse width modulated waveform (PWM) with a prescribed harmonic content. Multilevel PWM design plays a major role in many diverse engineering disciplines. In power electronics, multilevel PWM design corresponds to determining the inverter switching times and levels for selective harmonic elimination and harmonic compensation. In mechatronics, the same design corresponds to shaping input signals to damp residual vibrations in flexible structures. More generally, in most applications, the aim of PWM design is to minimize the total harmonic distortion while adhering to a prescribed harmonic content. The solution approach presented in this paper is based on linear programming with the objective of minimizing the total harmonic distortion. This objective is achieved within an arbitrarily small bound of the optimal solution. In addition, the linear programming formulation makes the design of such switching waveforms computationally tractable and efficient. Simulations are provided for corroboration.

eess.SY

Optimal input design for system identification using spectral decomposition

The aim of this paper is to design a band-limited optimal input with power constraints for identifying a linear multi-input multi-output system. It is assumed that the nominal system parameters are specified. The key idea is to use the spectral decomposition theorem and write the power spectrum as $\phi_{u}(j\omega)=\frac{1}{2}H(j\omega)H^*(j\omega)$. The matrix $H(j\omega)$ is expressed in terms of a truncated basis for $\mathcal{L}^2\left(\left[-\omega_{\mbox{cut-off}},\omega_{\mbox{cut-off}}\right]\right)$. With this parameterization, the elements of the Fisher Information Matrix and the power constraints turn out to be homogeneous quadratics in the basis coefficients. The optimality criterion used are the well-known $\mathcal{D}-$optimality, $\mathcal{A}-$optimality, $\mathcal{T}-$optimality and $\mathcal{E}-$optimality. The resulting optimization problem is non-convex in general. A lower bound on the optimum is obtained through a bi-linear formulation of the problem, while an upper bound is obtained through a convex relaxation. These bounds can be computed efficiently as the associated problems are convex. The lower bound is used as a sub-optimal solution, the sub-optimality of which is determined by the difference in the bounds. Interestingly, the bounds match in many instances and thus, the global optimum is achieved. A discussion on the non-convexity of the optimization problem is also presented. Simulations are provided for corroboration.

eess.SY