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Register a new userOn convergence of the optimization process in Radiotherapy treatment planning
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I. Hoveijn
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The Radiotherapy treatment planning optimization process based on a quasi-Newton algorithm with an object function containing dose-volume constraints is not guaranteed to converge when the dose value in the dose-volume constraint is a critical value of the dose distribution. This is caused by finite differentiability of the dose-volume histogram at such values. A closer look near such values reveals that convergence is most likely not at stake, but it might be slowed down.
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Purpose: A Monte Carlo (MC) beam model and its implementation in a clinical treatment planning system (TPS, Varian Eclipse) are presented for a modified ultra-high dose-rate electron FLASH radiotherapy (eFLASH-RT) LINAC. Methods: The gantry head without scattering foils or targets, representative of the LINAC modifications, was modelled in Geant4. The energy spectrum ({sigma}E) and beam source emittance cone angle ({theta}cone) were varied to match the calculated and Gafchromic film measured central-axis percent depth dose (PDD) and lateral profiles. Its Eclipse configuration was validated with measured profiles of the open field and nominal fields for clinical applicators. eFLASH-RT plans were MC forward calculated in Geant4 for a mouse brain treatment and compared to a conventional (Conv-RT) plan in Eclipse for a human patient with metastatic renal cell carcinoma. Results: The beam model and its Eclipse configuration agreed best with measurements at {sigma}E=0.5 MeV and {theta}cone=3.9+/-0.2 degrees to clinically acceptable accuracy (the absolute average error was within 1.5% for in-water lateral, 3% for in-air lateral, and 2% for PDD). The forward dose calculation showed dose was delivered to the entire mouse brain with adequate conformality. The human patient case demonstrated the planning capability with routine accessories in relatively complex geometry to achieve an acceptable plan (90% of the tumor volume receiving 95% and 90% of the prescribed dose for eFLASH and Conv-RT, respectively). Conclusion: To the best of our knowledge, this is the first functional beam model commissioned in a clinical TPS for eFLASH-RT, enabling planning and evaluation with minimal deviation from Conv-RT workflow. It facilitates the clinical translation as eFLASH-RT and Conv-RT plan quality were comparable for a human patient. The methods can be expanded to model other eFLASH irradiators.
In this paper, we study the global convergence of majorization minimization (MM) algorithms for solving nonconvex regularized optimization problems. MM algorithms have received great attention in machine learning. However, when applied to nonconvex optimization problems, the convergence of MM algorithms is a challenging issue. We introduce theory of the Kurdyka- Lojasiewicz inequality to address this issue. In particular, we show that many nonconvex problems enjoy the Kurdyka- Lojasiewicz property and establish the global convergence result of the corresponding MM procedure. We also extend our result to a well known method that called CCCP (concave-convex procedure).
Bilevel optimization has arisen as a powerful tool for many machine learning problems such as meta-learning, hyperparameter optimization, and reinforcement learning. In this paper, we investigate the nonconvex-strongly-convex bilevel optimization problem. For deterministic bilevel optimization, we provide a comprehensive convergence rate analysis for two popular algorithms respectively based on approximate implicit differentiation (AID) and iterative differentiation (ITD). For the AID-based method, we orderwisely improve the previous convergence rate analysis due to a more practical parameter selection as well as a warm start strategy, and for the ITD-based method we establish the first theoretical convergence rate. Our analysis also provides a quantitative comparison between ITD and AID based approaches. For stochastic bilevel optimization, we propose a novel algorithm named stocBiO, which features a sample-efficient hypergradient estimator using efficient Jacobian- and Hessian-vector product computations. We provide the convergence rate guarantee for stocBiO, and show that stocBiO outperforms the best known computational complexities orderwisely with respect to the condition number $kappa$ and the target accuracy $epsilon$. We further validate our theoretical results and demonstrate the efficiency of bilevel optimization algorithms by the experiments on meta-learning and hyperparameter optimization.
We previously proposed an intelligent automatic treatment planning framework for radiotherapy, in which a virtual treatment planner network (VTPN) was built using deep reinforcement learning (DRL) to operate a treatment planning system (TPS). Despite the success, the training of VTPN via DRL was time consuming. Also the training time is expected to grow with the complexity of the treatment planning problem, preventing the development of VTPN for more complicated but clinically relevant scenarios. In this study we proposed a knowledge-guided DRL (KgDRL) that incorporated knowledge from human planners to guide the training process to improve the training efficiency. Using prostate cancer intensity modulated radiation therapy as a testbed, we first summarized a number of rules of operating our in-house TPS. In training, in addition to randomly navigating the state-action space, as in the DRL using the epsilon-greedy algorithm, we also sampled actions defined by the rules. The priority of sampling actions from rules decreased over the training process to encourage VTPN to explore new policy that was not covered by the rules. We trained a VTPN using KgDRL and compared its performance with another VTPN trained using DRL. Both VTPNs trained via KgDRL and DRL spontaneously learned to operate the TPS to generate high-quality plans, achieving plan quality scores of 8.82 and 8.43, respectively. Both VTPNs outperformed treatment planning purely based on the rules, which had a plan score of 7.81. VTPN trained with 8 episodes using KgDRL was able to perform similarly to that trained using DRL with 100 episodes. The training time was reduced from more than a week to 13 hours. The proposed KgDRL framework accelerated the training process by incorporating human knowledge, which will facilitate the development of VTPN for more complicated treatment planning scenarios.
We consider the problem of optimizing the sum of a smooth convex function and a non-smooth convex function using proximal-gradient methods, where an error is present in the calculation of the gradient of the smooth term or in the proximity operator with respect to the non-smooth term. We show that both the basic proximal-gradient method and the accelerated proximal-gradient method achieve the same convergence rate as in the error-free case, provided that the errors decrease at appropriate rates.Using these rates, we perform as well as or better than a carefully chosen fixed error level on a set of structured sparsity problems.
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