arXiv subjects

Subhamon Supantha

Publications and source records attributed to Subhamon Supantha.

3 recordsLinked to original sources

arXiv2025

Universal Dynamic Regret and Constraint Violation Bounds for Constrained Online Convex Optimization

We consider a generalization of the celebrated Online Convex Optimization (OCO) framework with adversarial online constraints. In this problem, an online learner interacts with an adversary sequentially over multiple rounds. At the beginning of each round, the learner chooses an action from a convex decision set. After that, the adversary reveals a convex cost function and a convex constraint function. The goal of the learner is to minimize the cumulative cost while satisfying the constraints as tightly as possible. We present two efficient algorithms with simple modular structures that give universal dynamic regret and cumulative constraint violation bounds, improving upon state-of-the-art results. While the first algorithm, which achieves the optimal regret bound, involves projection onto the constraint sets, the second algorithm is projection-free and achieves better violation bounds in rapidly varying environments. Our results hold in the most general case when both the cost and constraint functions are chosen arbitrarily, and the constraint functions need not contain any fixed common feasible point. We establish these results by introducing a general framework that reduces the constrained learning problem to an instance of the standard OCO problem with specially constructed surrogate cost functions.

cs.LG↗

arXiv2025

Projection-free Algorithms for Online Convex Optimization with Adversarial Constraints

We study a generalization of the Online Convex Optimization (OCO) framework with time-varying adversarial constraints. In this setting, at each round, the learner selects an action from a convex decision set $X$, after which both a convex cost function and a convex constraint function are revealed. The objective is to design a computationally efficient learning policy that simultaneously achieves low regret with respect to the cost functions and low cumulative constraint violation (CCV) over a horizon of length $T$. A major computational bottleneck in standard OCO algorithms is the projection operation onto the decision set $X$. However, for many structured decision sets, linear optimization can be performed efficiently. Motivated by this, we propose a projection-free online conditional gradient (OCG)-based algorithm that requires only a single call to a linear optimization oracle over $X$ per round. Our approach improves upon the state of the art for projection-free online learning with adversarial constraints, achieving $\tilde{O}(T^{\frac{3}{4}})$ bounds for both regret and CCV. Our algorithm is conceptually simple. It constructs a surrogate cost function as a nonnegative linear combination of the cost and constraint functions, and feeds these surrogate costs into a novel adaptive online conditional gradient subroutine introduced in this paper. We further extend our framework to the bandit setting, where we show that a new form of surrogate loss is necessary to properly handle bandit feedback - an issue overlooked in prior work. Finally, we develop an efficient Follow-the-Perturbed-Leader (FTPL)-based algorithm, particularly well-suited for online combinatorial optimization problems with discrete actions, which also achieves $O(T^{\frac{3}{4}})$ regret and CCV.

cs.LG↗

arXiv2024

A Dynamic Agent Based Model of the Real Economy with Monopolistic Competition, Perfect Product Differentiation, Heterogeneous Agents, Increasing Returns to Scale and Trade in Disequilibrium

We have used agent-based modeling as our numerical method to artificially simulate a dynamic real economy where agents are rational maximizers of an objective function of Cobb-Douglas type. The economy is characterised by heterogeneous agents, acting out of local or imperfect information, monopolistic competition, perfect product differentiation, allowance for increasing returns to scale technology and trade in disequilibrium. An algorithm for economic activity in each period is devised and a general purpose open source agent-based model is developed which allows for counterfactual inquiries, testing out treatments, analysing causality of various economic processes, outcomes and studying emergent properties. 10,000 simulations, with 10 firms and 80 consumers are run with varying parameters and the results show that from only a few initial conditions the economy reaches equilibrium while in most of the other cases it remains in perpetual disequilibrium. It also shows that from a few initial conditions the economy reaches a disaster where all the consumer wealth falls to zero or only a single producer remains. Furthermore, from some initial conditions, an ideal economy with high wage rate, high consumer utility and no unemployment is also reached. It was also observed that starting from an equal endowment of wealth in consumers and in producers, inequality emerged in the economy. In majority of the cases most of the firms(6-7) shut down because they were not profitable enough and only a few firms remained. Our results highlight that all these varying outcomes are possible for a decentralized market economy with rational optimizing agents.

econ.TH↗