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Mohsen Amiri

Publications and source records attributed to Mohsen Amiri.

17 recordsLinked to original sources
arXiv2026

Reinforcement Learning in Switching Non-Stationary Markov Decision Processes: Algorithms and Convergence Analysis

We introduce the Switching Non-Stationary Markov Decision Process (SNS-MDP) framework, in which the environment transitions among a finite set of MDPs governed by a latent Markov chain while the agent observes only the external state. We show that the long-term effect of this switching is equivalent to stationary dynamics parameterized by the stationary distribution of the hidden Markov chain. For fixed policies, we derive a closed-form expression for the SNS value function and prove that standard temporal-difference (TD) learning converges to it almost surely despite persistent non-stationarity. We further establish that policy iteration converges to the optimal policy of the equivalent averaged environment, and prove that tabular Q-learning converges almost surely to the optimal Q-function. The framework is validated on a wireless communication network with Markovian channel noise, demonstrating its practical efficacy for decision-making in rapidly time-varying systems.

cs.LG↗
arXiv2026

On the Sum of Element Orders in Finite Abelian Groups

Let $ψ(G) = \sum_{g \in G} o(g)$ denote the sum of element orders of a finite group $G$. It is known that among groups of order $n$, the cyclic group $C_n$ maximizes $ψ$. Tărnăuceanu proved that two finite abelian $p$-groups of the same order are isomorphic if and only if they have the same sum of element orders, and conjectured this for arbitrary finite abelian groups. In this paper, we confirm the conjecture by proving a stronger result: for finite $LCM$-groups $G$ and $H$ of the same order, $ψ(G) = ψ(H)$ if and only if $G$ and $H$ have the same order type.

math.GR↗
arXiv2026

MARBLE: Multi-Armed Restless Bandits in Latent Markovian Environment

Restless Multi-Armed Bandits (RMABs) are powerful models for decision-making under uncertainty, yet classical formulations typically assume fixed dynamics, an assumption often violated in nonstationary environments. We introduce MARBLE (Multi-Armed Restless Bandits in a Latent Markovian Environment), which augments RMABs with a latent Markov state that induces nonstationary behavior. In MARBLE, each arm evolves according to a latent environment state that switches over time, making policy learning substantially more challenging. We further introduce the Markov-Averaged Indexability (MAI) criterion as a relaxed indexability assumption and prove that, despite unobserved regime switches, under the MAI criterion, synchronous Q-learning with Whittle Indices (QWI) converges almost surely to the optimal Q-function and the corresponding Whittle indices. We validate MARBLE on a calibrated simulator-embedded (digital twin) recommender system, where QWI consistently adapts to a shifting latent state and converges to an optimal policy, empirically corroborating our theoretical findings.

cs.LG↗
arXiv2026

PriPG-RL: Privileged Planner-Guided Reinforcement Learning for Partially Observable Systems with Anytime-Feasible MPC

This paper addresses the problem of training a reinforcement learning (RL) policy under partial observability by exploiting a privileged, anytime-feasible planner agent available exclusively during training. We formalize this as a Partially Observable Markov Decision Process (POMDP) in which a planner agent with access to an approximate dynamical model and privileged state information guides a learning agent that observes only a lossy projection of the true state. To realize this framework, we introduce an anytime-feasible Model Predictive Control (MPC) algorithm that serves as the planner agent. For the learning agent, we propose Planner-to-Policy Soft Actor-Critic (P2P-SAC), a method that distills the planner agent's privileged knowledge to mitigate partial observability and thereby improve both sample efficiency and final policy performance. We support this framework with rigorous theoretical analysis. Finally, we validate our approach in simulation using NVIDIA Isaac Lab and successfully deploy it on a real-world Unitree Go2 quadruped navigating complex, obstacle-rich environments.

cs.LG↗
arXiv2025

Challenger-Based Combinatorial Bandits for Subcarrier Selection in OFDM Systems

This paper investigates the identification of the top-m user-scheduling sets in multi-user MIMO downlink, which is cast as a combinatorial pure-exploration problem in stochastic linear bandits. Because the action space grows exponentially, exhaustive search is infeasible. We therefore adopt a linear utility model to enable efficient exploration and reliable selection of promising user subsets. We introduce a gap-index framework that maintains a shortlist of current estimates of champion arms (top-m sets) and a rotating shortlist of challenger arms that pose the greatest threat to the champions. This design focuses on measurements that yield the most informative gap-index-based comparisons, resulting in significant reductions in runtime and computation compared to state-of-the-art linear bandit methods, with high identification accuracy. The method also exposes a tunable trade-off between speed and accuracy. Simulations on a realistic OFDM downlink show that shortlist-driven pure exploration makes online, measurement-efficient subcarrier selection practical for AI-enabled communication systems.

cs.LG↗
arXiv2025

Safe and Efficient Robot Action Planning in the Presence of Unconcerned Humans

This paper proposes a robot action planning scheme that provides an efficient and probabilistically safe plan for a robot interacting with an unconcerned human -- someone who is either unaware of the robot's presence or unwilling to engage in ensuring safety. The proposed scheme is predictive, meaning that the robot is required to predict human actions over a finite future horizon; such predictions are often inaccurate in real-world scenarios. One possible approach to reduce the uncertainties is to provide the robot with the capability of reasoning about the human's awareness of potential dangers. This paper discusses that by using a binary variable, so-called danger awareness coefficient, it is possible to differentiate between concerned and unconcerned humans, and provides a learning algorithm to determine this coefficient by observing human actions. Moreover, this paper argues how humans rely on predictions of other agents' future actions (including those of robots in human-robot interaction) in their decision-making. It also shows that ignoring this aspect in predicting human's future actions can significantly degrade the efficiency of the interaction, causing agents to deviate from their optimal paths. The proposed robot action planning scheme is verified and validated via extensive simulation and experimental studies on a LoCoBot WidowX-250.

cs.RO↗
arXiv2025

REAP-T: A MATLAB Toolbox for Implementing Robust-to-Early Termination Model Predictive Control

This paper presents a MATLAB toolbox for implementing robust-to-early termination model predictive control, abbreviated as REAP, which is designed to ensure a sub-optimal yet feasible solution when MPC computations are prematurely terminated due to limited computational resources. Named REAP-T, this toolbox is a comprehensive, user-friendly, and modular platform that enables users to explore, analyze, and customize various components of REAP for their specific applications. Notable attributes of REAP-T are: (i) utilization of built-in MATLAB functions for defining the MPC problem; (ii) an interactive and intuitive graphical user interface for parameter tuning and visualization; (iii) real-time simulation capabilities, allowing users to observe and understand the real-time behavior of their systems; and (iv) inclusion of real-world examples designed to guide users through its effective use.

math.OC↗
arXiv2025

Practical Considerations for Implementing Robust-to-Early Termination Model Predictive Control

Model Predictive Control (MPC) is widely used to achieve performance objectives, while enforcing operational and safety constraints. Despite its high performance, MPC often demands significant computational resources, making it challenging to implement in systems with limited computing capacity. A recent approach to address this challenge is to use the Robust-to-Early Termination (REAP) strategy. At any time instant, REAP converts the MPC problem into the evolution of a virtual dynamical system whose trajectory converges to the optimal solution, and provides guaranteed sub-optimal and feasible solution whenever its evolution is terminated due to limited computational power. REAP has been introduced as a continuous-time scheme and its theoretical properties have been derived under the assumption that it performs all the computations in continuous time. However, REAP should be practically implemented in discrete-time. This paper focuses on the discrete-time implementation of REAP, exploring conditions under which anytime feasibility and convergence properties are maintained when the computations are performed in discrete time. The proposed methodology is validated and evaluated through extensive simulation and experimental studies.

math.OC↗
arXiv2024

On a bijection between a finite group to a non-cyclic group with divisibility of element orders

Consider a finite group $G$ of order $n$ with a prime divisor $p$. In this article, we establish, among other results, that if the Sylow $p$-subgroup of $G$ is neither cyclic nor generalized quaternion, then there exists a bijection $f$ from $G$ onto the abelian group $C_{\frac{n}{p}}\times C_p$ such that for every element $x$ in $G$, the order of $x$ divides the order of $f(x)$. This resolves Question 1.5 posed in [15]. As application of our results, we show that the group with the third largest value of the sum of element orders in the set of all finite groups of order $n$ is a solvable $p$-nilpotent group where $p$ is the smallest prime divisor of $n$ such that the Sylow $p$-subgroups are not cyclic.

math.GR↗
arXiv2024

Closed-Loop Model Identification and MPC-based Navigation of Quadcopters: A Case Study of Parrot Bebop 2

The growing potential of quadcopters in various domains, such as aerial photography, search and rescue, and infrastructure inspection, underscores the need for real-time control under strict safety and operational constraints. This challenge is compounded by the inherent nonlinear dynamics of quadcopters and the on-board computational limitations they face. This paper aims at addressing these challenges. First, this paper presents a comprehensive procedure for deriving a linear yet efficient model to describe the dynamics of quadrotors, thereby reducing complexity without compromising efficiency. Then, this paper develops a steady-state-aware Model Predictive Control (MPC) to effectively navigate quadcopters, while guaranteeing constraint satisfaction at all times. The main advantage of the steady-state-aware MPC is its low computational complexity, which makes it an appropriate choice for systems with limited computing capacity, like quadcopters. This paper considers Parrot Bebop 2 as the running example, and experimentally validates and evaluates the proposed algorithms.

cs.RO↗
arXiv2023

Finite solvable groups with a nilpotent normal complement subgroup

Let $G$ be a finite solvable group and $H$ a non-normal core-free subgroup of $G$. We show that if the normalizer of any non-trivial normal subgroup of $Fit(H)$ is equal $H$, then $H$ has a nilpotent normal complement $K$ such that $G=KH$ and $KZ(Fit(H))$ is a Frobenius group.

math.GR↗
arXiv2021

Finite unitary rings with a single subgroup of prime order of the group of units

Let R be a unitary ring of finite cardinality P^k, where p is a prime number and $p\nmid k$. We show that if the group of units of $R$ has at most one subgroup of order $p$, then $R\cong A\bigoplus B,$ where $B$ is a finite ring of order $k$ and $A$ is a ring of cardinality $p^β$ which is one of the six explicitly described types.

math.RA↗
arXiv2020

Finite unitary ring with minimal non-nilpotent group of units

Let $R$ be a finite unitary ring such that $R=R_0[R^*]$ where $R_0$ is the prime ring and $R^*$ is not a nilpotent group. We show that if all proper subgroups of $R^*$ are nilpotent groups, then the cardinal of $R$ is a power of prime number 2. In addition, if $(R/Jac(R))^*$ is not a $p-$group, then either $R\cong M_2(GF(2))$ or $R\cong M_2(GF(2))\oplus A$ where $M_2(GF(2))$ is the ring of $2\times 2$ matrices over the finite field $GF(2)$ and $A$ is a direct sum of finite field $GF(2)$.

math.RA↗
arXiv2019

Characterization of P-groups By Sum of Element Orders

Let $G$ be a finite group. Then we denote $ψ(G) = \sum_{x\in G}o(x)$ where $o(x)$ is the order of the element $x$ in $G$. In this paper we characterize some finite $p$-groups ($p$ a prime) by $ψ$ and their orders.

math.GR↗