Algorithms for Optimal Paths of One, Many, and an Infinite Number of Agents

In this dissertation, we provide efficient algorithms for modeling the behavior of a single agent, multiple agents, and a continuum of agents. For a single agent, we combine the modeling framework of optimal control with advances in optimization splitting in order to efficiently find optimal paths for problems in very high-dimensions, thus providing alleviation from the curse of dimensionality. For a multiple, but finite, number of agents, we take the framework of multi-agent reinforcement learning and utilize imitation learning in order to decentralize a centralized expert, thus obtaining optimal multi-agents that act in a decentralized fashion. For a continuum of agents, we take the framework of mean-field games and use two neural networks, which we train in an alternating scheme, in order to efficiently find optimal paths for high-dimensional and stochastic problems. These tools cover a wide variety of use-cases that can be immediately deployed for practical applications

Wasserstein Diffusion Tikhonov Regularization

We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and define a corresponding input-dependent additive noise data augmentation model. Expanding and integrating the augmented loss yields an effective Tikhonov-type Wasserstein diffusion smoothness regularizer. This approach allows us to apply high levels of regularization and train functions that have low variability within classes but remain flexible across classes. We provide efficient methods for computing the regularizer at a negligible cost in comparison to training with adversarial data augmentation. Initial experiments demonstrate improvements in generalization performance under adversarial perturbations and also large in-class variations of the input data

Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games

We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are beyond reach with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex-concave saddle point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN). We show the potential of our method on up to 100-dimensional MFG problems

Primary Urothelial Carcinoma of the Ureter: 11-Year Experience in Taipei Veterans General Hospital

BackgroundUrothelial carcinoma of the upper urinary tract is relatively rare, occurring in 5% of all urothelial tumors. Ureteral urothelial carcinoma is even less common than that of the renal pelvis, accounting for about 25% of all upper urinary tract tumors. The aim of this study was to evaluate the clinical behavior, survival, recurrence and prognostic information of primary ureteral urothelial carcinoma from our 11 years of experience at the Taipei Veterans General Hospital.MethodsWe retrospectively reviewed 111 patients with ureteral urothelial carcinoma who had been treated in our hospital between January 1993 and December 2003. Tumor staging was according to the 2002 AJCC TNM classification and stage groupings. Patients with stage 0a and stage 0is were categorized as stage 0a/is, and patients with pathologic T stage pTa and pTis were categorized as pTa/is for statistical analysis. The Kaplan-Meier method was used for survival analysis.ResultsThere were 69 males and 42 females, with a mean age of 70.5 ± 9.4 years at diagnosis. Of the 111 patients, 5 presented with stage 0a/is, 38 with stage I, 23 with stage II, 21 with stage III, and 24 with stage IV. Nephroureterectomy with bladder cuff excision was performed in 78 patients, 12 patients received segmental resection of the ureter, 4 received ureteroscopic laser coagulation, and 17 underwent chemotherapy or radiotherapy or both. Tumors were located on the left side in 53 patients, on the right in 53, and bilaterally in 5. The most frequent initial presenting symptom was gross hematuria (65%). The mean postoperative follow-up period was 49.3 months. Disease recurrence in the nephroureterectomy group occurred in 36 patients (46.2%), with 17 (21.8%) at the urinary bladder, 2 (2.6%) at the retroperitoneum, 1 (1.3%) at the contralateral ureter, 6 (7.7%) with distant metastases to the lung, bone, distant lymph nodes or liver, and 10 (12.8%) at multiple sites. The 5-year cancer-specific survival rate was 100% for pTa/is, 95.2% for pT1, 69.4% for pT2, and 43.8% for pT3. All 3 pT4 cases died of cancer in a median of 12 months. Significant prognostic factors for cancer-specific survival by univariate analysis were pT (p = 0.00001), stage (p = 0.00001), type of treatment (p = 0.00001) and grade (p = 0.0001). On multivariate analysis, only stage (p = 0.0001) and grade (p = 0.014) were significant for cancer-specific and overall survival. Stage (p = 0.0001), pT (p =0.0001) and grade (p = 0.026) were also significant prognostic factors of recurrence in multivariate analysis.ConclusionOur experience showed that patients with pTa/is and pT1 tumors treated with radical surgery have excellent prognoses. Tumor stage and grade are the only significant prognostic factors for both cancer-specific and overall survival