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Safe Learning of Adaptive Control Policies for Remote Patient Monitoring

Ramanan Tamizholi, Siddharth Chandak, Isha Thapa, Nicholas Bambos, David Scheinker

arXiv:2610.10720v1eess.SYcs.SY

TL;DR

RPM monitoring must balance patient safety and monitoring burden, and system parameters may be unknown at deployment. The paper uses online model-based reinforcement learning to estimate parameters and adapt monitoring thresholds while prioritizing safety during exploration. Theory and simulations report convergence to the optimal threshold policy alongside safe monitoring and low overall costs.

  • Problem

    RPM must balance monitoring intensity against patient safety and costs, while unknown parameters and changing guidelines complicate safe adaptation during deployment.

    Source: §I · p. 1

  • Method

    An online model-based reinforcement learning algorithm estimates system parameters and adapts monitoring thresholds using randomized exploration designed to prioritize safety.

    Source: §I · p. 1, §III · p. 4, §V · p. 5

  • Results

    Theoretical guarantees and simulations show convergence to the optimal threshold policy, safe monitoring decisions, and low overall costs.

    Source: §III · p. 4, A. Safety Considerations · p. 4, §V · p. 6

  • Takeaways & Limitations

    The framework is presented as a flexible approach to adaptive monitoring that can adjust to evolving patient data, institutional constraints, and clinical guidelines without prior knowledge.

    Source: §I · pp. 1–2

Abstract

from arXiv · show

Remote Patient Monitoring (RPM) enables continuous observation of patients in their daily environments, improving both health outcomes and quality of life. A key challenge in RPM is determining the optimal monitoring intensity, while balancing patient safety and monitoring costs. This problem is further complicated when system parameters, such as transition probabilities and costs, are initially unknown. We develop a learning-based control framework that estimates these parameters and adapts the monitoring policy in real time. The proposed approach is an online model-based reinforcement learning algorithm tailored to RPM, with patient safety explicitly prioritized during exploration. We provide theoretical guarantees on safety and convergence to the optimal policy. Simulation results show that the algorithm converges to the optimal threshold-based policy, maintains low treatment costs, and reduces the risk of patients reaching critical health states.

I. INTRODUCTION

RPM offers continuous observation in daily life, but choosing monitoring intensity requires balancing health support against patient burden and provider workload. This paper develops a learning approach for adapting monitoring policies when system parameters are unknown, while prioritizing safety during exploration.

I. INTRODUCTION

  • RPM makes continuous observation possible, but monitoring intensity must balance health support against patient burden and provider workload.Intensive monitoring may support earlier detection but can increase treatment burden or fatigue; less intensive monitoring may provide insufficient support.Source: §I · p. 1
  • Earlier MDP analyses found threshold policies optimal but assumed clinicians knew transition probabilities and patient costs in advance.Those analyses studied how the optimal policy depends on health-improvement probabilities, monitoring options, and invasiveness costs.Source: §I · p. 1
  • Unknown parameters and changing clinical guidelines make safe adaptation during deployment an important challenge for RPM monitoring.New interventions may lack historical data, while RPM data streams create opportunities to adapt strategies based on observed outcomes.Source: §I · p. 1
  • The paper formulates monitoring control as reinforcement learning, learning system parameters while adapting the policy in real time.The focus is when to intensively observe patients, rather than automating treatment decisions.Source: §I · p. 1
  • The approach uses randomized threshold exploration and, with appropriate initialization, guarantees safety during learning and convergence to the optimal threshold policy under mild assumptions.The authors describe the resulting support tool as interpretable and retaining clinician oversight.Source: §I · pp. 1–2

II. THE REMOTE PATIENT MONITORING MODEL

The RPM model represents each patient through a health state and a monitoring state at each service period. Monitoring options carry treatment-burden costs, while the lowest health state marks the boundary of the modeled service.

II. THE REMOTE PATIENT MONITORING MODEL

  • At each service period, the patient has a health state and an ordinary or intensive monitoring state, which together form the system state.Intensive monitoring includes downstream clinical responses enabled by increased observation and can lead to improved health outcomes.Source: §II · p. 2
  • Higher health-state values indicate better health, while state 0 is critical and ends service-model evolution, requiring emergency or more severe interventions.Source: §II · p. 2
  • Ordinary and intensive monitoring incur constant costs Co and Ci, respectively, interpreted here as invasiveness burdens on everyday life and quality of life.A significant critical-state cost Cc is incurred in states where the model ceases to apply.Source: §II · p. 2

A. Markov Decision Process

The RPM service is modeled as an MDP with monitoring state and health state governing transitions and costs. The model assumes intensive monitoring improves health faster, while monitoring and critical-state costs are ordered by burden and severity.

A. Markov Decision Process

  • The service is modeled as an MDP with ordinary or intensive actions, state-dependent costs, and transition probabilities between service states.At health state 0, no action is taken, the state is absorbing, and cost Cc is incurred.Source: A. Markov Decision Process · p. 2
  • Without switching, health moves up or down by one state under the current monitoring mode, with transition probabilities λ and 1−λ and its associated monitoring cost.The upper health boundary H caps upward movement.Source: A. Markov Decision Process · p. 2
  • Switching changes the monitoring state, and the resulting transition probabilities and costs match those for the destination monitoring mode.The switching decision occurs at the beginning of the time step.Source: A. Markov Decision Process · p. 2
  • The assumptions are that intensive monitoring has at least as high a health-improvement probability as ordinary monitoring, and costs satisfy 0 ≤ Co ≤ Ci ≤ Cc.The text motivates the cost ordering by greater burden under intensive monitoring and the severity of entering the critical state.Source: A. Markov Decision Process · p. 2

B. Optimal Monitoring Control

The control objective minimizes expected discounted patient costs until the critical state is reached. Under stated conditions, the optimal monitoring policy has a threshold form, reducing the search to a single threshold.

B. Optimal Monitoring Control

  • The objective is to minimize expected discounted costs, with the critical-state cost discounted according to the time the patient reaches that state.The discount factor is γ, with 0 < γ < 1.Source: B. Optimal Monitoring Control · pp. 2–3
  • A threshold policy uses intensive monitoring at health levels at or below its threshold and ordinary monitoring above it.Figure 1b illustrates a threshold of 3, with intensive monitoring for h ≤ 3 and ordinary monitoring for h > 3.Source: B. Optimal Monitoring Control · p. 3, Figure 1 · p. 3
  • When H and 1/γ are sufficiently large, the optimal policy is threshold-based for some threshold between 0 and H.Source: B. Optimal Monitoring Control · p. 3
  • The threshold result reduces the optimization to identifying the optimal threshold, and the authors report numerical corroboration in prior studies.The passage cites, for that corroboration.Source: B. Optimal Monitoring Control · p. 3

III. LEARNING THE UNKNOWN RPM MODEL

The framework learns unknown RPM transition and cost parameters from patient data during deployment, then updates monitoring policies online. Its threshold-based exploration supports interpretable adaptation while prioritizing safety and converging to the optimal policy under mild assumptions.

III. LEARNING THE UNKNOWN RPM MODEL

  • The algorithm learns unknown costs and transition probabilities from observations of patients receiving RPM and continually updates its control policy.This is framed as online reinforcement learning rather than treatment automation.Source: §III · p. 3
  • Each epoch updates model parameters, computes a policy from current estimates, and applies it to patients while collecting cost and health-transition samples.Epochs are fixed time periods, during which the policy is applied to the enrolled patient population.Source: §III · pp. 3–4
  • Counts of monitoring actions, health improvements, and incurred costs estimate action-specific transition probabilities and costs, using priors and prior strength for initialization.Cost samples may come from patient surveys, while transition probabilities are estimated from observed health changes.Source: §III · pp. 3–4
  • When the estimated optimal threshold is outside hlow or hhigh, the deployed threshold may move to that clinically meaningful level with probability ρk.The slowly decreasing probability encourages more exploration early and greater reliance on the estimated optimum as estimates improve.Source: §III · p. 4
  • Threshold-based exploration uses fragile and sufficiently good health states rather than arbitrary state-action perturbations, and the resulting policy converges almost surely to the optimum under mild assumptions.Theorem 2 states that Algorithm 1's deployed threshold converges almost surely to the optimal threshold.Source: §III · p. 4

A. Safety Considerations

The safety guarantee depends on conservative initialization: priors and prior strength shape early deployed thresholds. Under the stated conditions, the deployed threshold stays at least as high as the optimal threshold with high probability throughout learning.

A. Safety Considerations

  • Priors determine the initial policy before enough data accrue, while larger prior strength slows updates and keeps the policy closer to its conservative initial form.The suggested prior relationship makes intensive monitoring more favorable, delaying critical states at higher monitoring cost.Source: A. Safety Considerations · p. 4
  • With conservative priors and sufficiently large prior strength, the deployed threshold is at least the optimal threshold in every epoch with probability at least 1 − δ.Theorem 3 requires n0 ≥ Ω(log(1/δ)).Source: A. Safety Considerations · p. 4
  • The guarantee measures safety by time to the critical state, and raising low estimated thresholds to hlow with probability ρk provides an additional safeguard during learning.The safety passage describes this adjustment as reducing the likelihood of overly aggressive low-threshold policies.Source: A. Safety Considerations · p. 5

IV. PERFORMANCE

In simulations, the algorithm reached an optimal or near-optimal policy within a few epochs in almost all runs, even before parameter estimates fully converged. Results also show robustness to initialization and fewer severe threshold violations with stronger prior strength.

IV. PERFORMANCE

  • Within a few epochs, the algorithm converged to an optimal or near-optimal policy in almost all runs, before parameter estimates necessarily fully converged.The reported threshold-policy robustness means slower parameter convergence had little practical impact.Source: §IV · p. 5
  • In 100 runs with n0 = 100, the threshold fell below h⋆ in 50 runs, below h⋆−1 in one, and below h⋆−2 or hlow in none.Table I counts runs with at least one threshold violation; larger prior strengths further reduced violation frequency.Source: Table I · p. 5, §IV · p. 5
  • Across initial thresholds, the algorithm reached the optimal policy at approximately the same number of epochs, while sufficiently large prior strengths kept average time to the critical state consistently high.The paper reports this as evidence of robustness to initialization and maintained safety during adaptation.Source: §IV · p. 5

V. CONCLUSIONS AND EXTENSIONS

The paper presents an online model-based reinforcement learning approach for RPM with initially unknown parameters. It reports convergence to the optimal threshold policy and identifies clinical validation and health-state-independent parameters as important boundaries.

V. CONCLUSIONS AND EXTENSIONS

  • The approach combines parameter estimation with exploration to optimize RPM policies when system parameters are initially unknown.Source: §V · p. 5
  • Figure 3 groups the first five patients to enter the system, then subsequent groups of five, for reporting rather than as synchronous cohorts.Patients within each group may enter and leave at different times.Source: Figure 3 · p. 6
  • The algorithm learns transition probabilities and costs, converges to the optimal threshold policy, and maintains low overall costs and safe monitoring decisions.Simulations also show convergence to threshold h̄ = 12 across initial thresholds and consistently high average time to critical health for sufficiently large prior strengths.Source: §V · p. 6
  • Testing on real-world patient data remains a next step for assessing practical performance and real-world variability and noise.The paper says such validation is needed to guide integration into RPM workflows and clinical deployment.Source: §V · p. 6
  • The analysis focuses on RPM parameters independent of health state; extensions to state-dependent parameters are practical only for small state spaces as parameters and sample needs grow.The paper identifies the resulting curse of dimensionality as future work.Source: §V · p. 6

APPENDIX I PROOF FOR THEOREM 1

The appendix proof reduces verification of a condition to equation (3), while the convergence result establishes eventual deployment of the optimal threshold under stated assumptions. Those assumptions include conditions on the health-state model, parameter stability, observation noise, and exploration.

APPENDIX I PROOF FOR THEOREM 1

  • The proof invokes prior threshold-optimality results and reduces verification to condition (3), which is satisfied for sufficiently large 1/γ.Source: Appendix I · p. 7

APPENDIX II CONVERGENCE GUARANTEES

  • Convergence assumes finite health states, positive upward and downward movement probabilities, a locally stable unique optimal threshold, and sub-Gaussian observation noise.It also assumes boundary-threshold exploration when the computed threshold falls outside [h_low, h_high].Source: APPENDIX II CONVERGENCE GUARANTEES · p. 7
  • Under Assumptions 2–5 and h_low ≤ h⋆ ≤ h_high, the deployed threshold eventually equals the optimal threshold almost surely.Theorem 4 states this holds from an almost surely finite random epoch onward.Source: APPENDIX II CONVERGENCE GUARANTEES · p. 7

A. Proof

The proof establishes that the algorithm’s parameter estimates converge almost surely and that its computed and deployed thresholds eventually equal the optimal threshold. Under additional assumptions, it also guarantees with probability at least 1 − δ that deployed thresholds never fall below the optimum.

A. Proof

  • Each action receives infinitely many real samples almost surely, enabling the proof of consistent parameter estimates.The proof uses the nonempty state regions induced by bounded thresholds and a positive lower bound on one-step transition probabilities.Source: A. Proof · pp. 7–8
  • Almost surely, parameter estimates converge to their true values, after which the computed threshold equals h⋆ at every epoch.Once the computed threshold is optimal and lies between hlow and hhigh, the deployed threshold also equals h⋆.Source: A. Proof · p. 8

APPENDIX III SAFETY GUARANTEES

  • With probability at least 1 − δ, the deployed threshold is at least h⋆ at every epoch under the theorem’s stated assumptions.These include Assumptions 4–7, hlow ≤ h⋆ ≤ hhigh, and a sufficiently large prior strength n0.Source: APPENDIX III SAFETY GUARANTEES · p. 8, A. Proof · p. 9

APPENDIX IV EXPERIMENT DETAILS

The appendix specifies simulation settings and the quantities varied in plots and a safety table. The supplied passages describe experimental designs, not their numerical outcomes.

APPENDIX IV EXPERIMENT DETAILS

  • Figure 2 reports the percentage of converged runs by epoch, varying initial thresholds or prior strengths.The prior-strength conditions are n0 ∈ {10, 100, 200, 500, 1000}; the initial-threshold conditions include 16 and 20, 18, 16, or 14 across the listed prior settings.Source: APPENDIX IV EXPERIMENT DETAILS · p. 9
  • Across the experiments, H = 20, λo = 0.2, λi = 0.55, Co = 0, Ci = 25, Cc = 50000, γ = 0.9, and the optimal threshold is 12.Each epoch consists of 75 timesteps.Source: APPENDIX IV EXPERIMENT DETAILS · p. 9
  • Figure 3 reports average time to reach critical health, comparing different initial thresholds and prior strengths.The listed initial thresholds are 16 for the baseline prior setting and 20, 18, 16, or 14 for the varying Ci,p settings.Source: APPENDIX IV EXPERIMENT DETAILS · p. 9
  • Table 1 reports the safety of the deployed policy for different priors.Source: APPENDIX IV EXPERIMENT DETAILS · p. 9
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