Recently deep learning has successfully achieved state-of-the-art performance on many difficult tasks. Deep neural network outperforms many existing popular methods in the field of reinforcement learning. It can also identify important covariates automatically. Parameter sharing of convolutional neural network (CNN) greatly reduces the amount of parameters in the neural network, which allows for high scalability. However few research has been done on deep advantage learning (A-learning). In this paper, we present a deep A-learning approach to estimate optimal dynamic treatment regime. A-learning models the advantage function, which is of direct relevance to the goal. We use an inverse probability weighting (IPW) method to estimate the difference between potential outcomes, which does not require to make any model assumption on the baseline mean function. We implemented different architectures of deep CNN and convexified convolutional neural networks (CCNN). The proposed deep A-learning methods are applied to a data from the STAR*D trial and are shown to have better performance compared with the penalized least square estimator using a linear decision rule.

Rationale: Percutaneous endoscopic lumbar discectomy (PELD) is an effective treatment for lumbar disc herniation and postoperative discal pseudocyst (PDP) can rarely develop after PELD. Patient concerns: A 30-year-old man experienced low back pain and pain in the right lower extremity for 1 month, which aggravated for 3 days. Diagnoses: Preoperative CT and MRI showed lumbar disc herniation at the L4/5 level. Then the patient underwent PELD under local anesthesia and his symptoms disappeared immediately after surgery. After 37 days of PELD, the patient complained of recurrent low back pain on the right side, and pain on the outer side of his lower leg. MR imaging revealed cystic mass with low signal on T1-weighted images (T1WI), and high signal on T2-weighted images (T2WI). The patient was diagnosed with a symptomatic PDP after PELD. Interventions: Initially, the patient was treated with conservative treatment, including administration of aescin and mannitol by intravenous infusion, physical therapy, sacral canal injection. Then he underwent discography at L4/5 and ozone ablation under local anesthesia. Outcomes: The patient's condition improved significantly after 1 week of surgery and was discharged. One-year and 3-month follow-up revealed no recurrence of low back pain and leg pain. Lessons: PDP is one of the rare complications of PELD, usually occurs in young patients. Patients with PDP have a low signal intensity on T1WI and high signal intensity on T2WI, which can be treated by conservative treatment, interventional therapy, and surgical treatment.

Building an effective portfolio is critical for it can decrease investment risk and the impact of fluctuations in the share price of a single firm. This paper selects five example stocks from diverse industries, using the mean variance model and the Index model to estimate the best combination of these stocks, then adds five significant limits to both models to see how components in the real financial market effect the portfolio. The Minimal Variance Frontier is used to compare the impact of five constraints in this paper, and it is discovered that different models have different effects under the same constraints, constrained portfolios have less volatility than unconstrained portfolios, and not allowing short positions reduces risk while also lowering the overall return rate. The findings in this paper are valuable to the industry's research on the best allocation of financial assets and can benefit financial market investors.