Near-Optimal Pure Exploration in Matrix Games: A Generalization of Stochastic Bandits & Dueling Bandits

We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. Formally, we are given a stochastic model where any learner can sample an entry $(i,j)$ of the input matrix $A\in[-1,1]^{n\times m}$ and observe $A_{i,j}+\eta$ where $\eta$ is a zero-mean 1-sub-Gaussian noise. The aim of the learner is to identify the PSNE of $A$, whenever it exists, with high probability while taking as few samples as possible. Zhou et al. (2017) presents an instance-dependent sample complexity lower bound that depends only on the entries in the row and column in which the PSNE lies. We design a near-optimal algorithm whose sample complexity matches the lower bound, up to log factors. The problem of identifying the PSNE also generalizes the problem of pure exploration in stochastic multi-armed bandits and dueling bandits, and our result matches the optimal bounds, up to log factors, in both the settings.Comment: 22 pages, 5 figure

Query-Efficient Algorithms to Find the Unique Nash Equilibrium in a Two-Player Zero-Sum Matrix Game

We study the query complexity of identifying Nash equilibria in two-player zero-sum matrix games. Grigoriadis and Khachiyan (1995) showed that any deterministic algorithm needs to query $\Omega(n^2)$ entries in worst case from an $n\times n$ input matrix in order to compute an $\varepsilon$-approximate Nash equilibrium, where $\varepsilon<\frac{1}{2}$. Moreover, they designed a randomized algorithm that queries $\mathcal O(\frac{n\log n}{\varepsilon^2})$ entries from the input matrix in expectation and returns an $\varepsilon$-approximate Nash equilibrium when the entries of the matrix are bounded between $-1$ and $1$. However, these two results do not completely characterize the query complexity of finding an exact Nash equilibrium in two-player zero-sum matrix games. In this work, we characterize the query complexity of finding an exact Nash equilibrium for two-player zero-sum matrix games that have a unique Nash equilibrium $(x_\star,y_\star)$. We first show that any randomized algorithm needs to query $\Omega(nk)$ entries of the input matrix $A\in\mathbb{R}^{n\times n}$ in expectation in order to find the unique Nash equilibrium where $k=|\text{supp}(x_\star)|$. We complement this lower bound by presenting a simple randomized algorithm that, with probability $1-\delta$, returns the unique Nash equilibrium by querying at most $\mathcal O(nk^4\cdot \text{polylog}(\frac{n}{\delta}))$ entries of the input matrix $A\in\mathbb{R}^{n\times n}$. In the special case when the unique Nash Equilibrium is a pure-strategy Nash equilibrium (PSNE), we design a simple deterministic algorithm that finds the PSNE by querying at most $\mathcal O(n)$ entries of the input matrix.Comment: 17 page

The Effect of a Low-Fat, Plant-Based Lifestyle Intervention (CHIP) on Serum HDL Subfraction Levels - A Cohort Study

This conference abstract discusses a low-fat plant-based diet and the effect it has on HDL level

When Does Size Matter? An Empirical Study of Consumer Demographics and Product Package Choices

From the Washington University Senior Honors Thesis Abstracts (WUSHTA), 2017. Published by the Office of Undergraduate Research. Joy Zalis Kiefer, Director of Undergraduate Research and Associate Dean in the College of Arts & Sciences; Lindsey Paunovich, Editor; Helen Human, Programs Manager and Assistant Dean in the College of Arts and Sciences Mentor: Tat Cha

HDL Subfraction Changes with a Low-fat, Plant-based Complete Health Improvement Program (CHIP)

Background and Objectives: Low HDL concentrations are considered an important risk factor for cardiovascular disease. Interventions promoting a low-fat, plant-based eating pattern appear to reduce CVD risk while paradoxically also reducing HDL concentrations. Recent studies show HDL to comprise a range of subfractions, but the role these play in ameliorating the risk of CVD is unclear. The purpose of this study was to characterise changes in HDL subfractions in participants where HDL decreased following the CHIP intervention which promotes a low-fat, plant-based diet, with physical activity. Methods and Study Design: Individuals (n=22; mean age=55.4±16.3 years; 45.5% men, 54.5% women) participating in a CHIP intervention were assessed at baseline and 30 days for changes in BMI, blood pressure, lipid profile, (including large-, intermediate- and small-HDL subfractions) and fasting glucose. Results: HDL significantly decreased (10.6%, pConclusions: This paper discusses specific changes in HDL subfractions when overall-HDL decreases as a response to low fat, whole-food, plant-based eating and exercise. Additional research is required to elucidate the reasons through which behavioural therapies remodel the HDL particle and how this impacts the functional properties of HDL and CVD risk

The Effect of a Low-Fat, Plant-Based Lifestyle Intervention (CHIP) on Serum HDL Levels and the Implications for Metabolic Syndrome Status - A Cohort Study

Background Low levels of high-density lipoproteins (HDL) are considered an important risk factor for cardiovascular disease and constitute one of the criteria for the Metabolic Syndrome (MetS). Lifestyle interventions promoting a low-fat, plant-based eating pattern appear to paradoxically reduce cardiovascular risk but also HDL levels. This study examined the changes in MetS risk factors, in particular HDL, in a large cohort participating in a 30-day lifestyle intervention that promoted a low-fat, plant-based eating pattern. Methods Individuals (n = 5,046; mean age = 57.3 ± 12.9 years; 33.5% men, 66.5% women) participating in a in a Complete Health Improvement Program (CHIP) lifestyle intervention within the United States were assessed at baseline and 30 days for changes in body mass index (BMI), blood pressure (BP), lipid profile and fasting plasma glucose (FPG). Results HDL levels decreased by 8.7% (p Conclusions When people move towards a low-fat, plant-based diet, HDL levels decrease while other indicators of cardiovascular risk improve. This observation raises questions regarding the value of using HDL levels as a predictor of cardiovascular risk in populations who do not consume a typical western diet. As HDL is part of the assemblage of risk factors that constitute MetS, classifying individuals with MetS may not be appropriate in clinical practice or research when applying lifestyle interventions that promote a plant-based eating pattern.[from publisher\u27s website]

Facility-level intervention to improve attendance and adherence among patients on anti-retroviral treatment in Kenya—a quasi-experimental study using time series analysis

Background: Achieving high rates of adherence to antiretroviral therapy (ART) in resource-poor settings comprises serious, but different, challenges in both the first months of treatment and during the life-long maintenance phase. We measured the impact of a health system-oriented, facility-based intervention to improve clinic attendance and patient adherence. Methods: This was a quasi-experimental, longitudinal, controlled intervention study using interrupted time series analysis. The intervention consisted of (1) using a clinic appointment diary to track patient attendance and monitor monthly performance; (2) changing the mode of asking for self-reported adherence; (3) training staff on adherence concepts, intervention methods, and use of monitoring data; (4) conducting visits to support facility teams with the implementation. We conducted the study in 12 rural district hospitals (6 intervention, 6 control) in Kenya and randomly selected 1894 adult patients over 18 years of age in two cohorts: experienced patients on treatment for at least one year, and newly treated patients initiating ART during the study. Outcome measures were: attending the clinic on or before the date of a scheduled appointment, attending within 3 days of a scheduled appointment, reporting perfect adherence, and experiencing a gap in medication supply of more than 14 days. Results: Among experienced patients, the percentage attending the clinic on or before a scheduled appointment increased in both level (average total increase immediately after intervention) (+5.7%; 95% CI = 2.1, 9.3) and trend (increase per month) (+1.0% per month; 95% CI = 0.6, 1.5) following the intervention, as did the level and trend of those keeping appointments within three days (+4.2%; 95% CI = 1.6, 6.7; and +0.8% per month; 95% CI = 0.6, 1.1, respectively). The relative difference between the intervention and control groups based on the monthly difference in visit rates increased significantly in both level (+6.5; 95% CI = 1.4, 11.6) and trend (1.0% per month; 95% CI = 0.2, 1.8) following the intervention for experienced patients attending the clinic within 3 days of their scheduled appointments. The decrease in the percentage of experienced patients with a medication gap greater than 14 days approached statistical significance (-11.3%; 95% CI = -22.7, 0.1), and the change seemed to persist over 11 months after the intervention. All facility staff used appointment-keeping data to calculate adherence and discussed outcomes regularly. Conclusion: The appointment-tracking system and monthly performance monitoring was strengthened, and patient attendance was improved. Scale-up to national level may be considered

Real world uptake, safety profile and outcomes of docetaxel in newly diagnosed metastatic prostate cancer

Objectives: To investigate the uptake, safety and efficacy of docetaxel chemotherapy in hormone-naïve metastatic prostate cancer (mPC) in the first year of use outside of a clinical trial. Subjects/patients and Methods: Patients in the West of Scotland Cancer Network (WoSCAN) with newly diagnosed mPC were identified from the regional multidisciplinary team (MDT) meetings and their treatment details were collected from electronic patient records. The rate of febrile neutropenia, hospitalisations, time to progression and overall survival were compared between those patients who received docetaxel and androgen deprivation therapy (ADT), or ADT alone using survival analysis. Results: Out of 270 eligible patients, 103 received docetaxel (38.1%). 35 patients (34%) were hospitalised and there were 17 episodes of febrile neutropenia (16.5%). Two patients (1.9%) died within 30 days of chemotherapy. Patients who received ADT alone had an increased risk of progression (HR 2.03, 95% CI (1.27, 3.25), log-rank test, p= 0.002) and had an increased risk of death (HR 5.88, 95% CI 2.52, 13.72, log-rank p=0.001) compared to the docetaxel group. The risk of febrile neutropenia was nine times greater if chemotherapy was started within three weeks of ADT initiation (95% CI (1.22,77.72) p= 0.032). Conclusion: Docetaxel chemotherapy in hormone-naïve mPC has significant toxicities, but has a similar effect on time to progression and overall survival as seen in randomised trials. Chemotherapy should be started 3 weeks or more after androgen deprivation

FGFR3 expression in primary and metastatic urothelial carcinoma of the bladder

While fibroblast growth factor receptor 3 (FGFR3) is frequently mutated or overexpressed in nonmuscle-invasive urothelial carcinoma (UC), the prevalence of FGFR3 protein expression and mutation remains unknown in muscle-invasive disease. FGFR3 protein and mRNA expression, mutational status, and copy number variation were retrospectively analyzed in 231 patients with formalin-fixed paraffin-embedded primary UCs, 33 metastases, and 14 paired primary and metastatic tumors using the following methods: immunohistochemistry, NanoString nCounterTM, OncoMap or Affymetrix OncoScanTM array, and Gain and Loss of Analysis of DNA and Genomic Identification of Significant Targets in Cancer software. FGFR3 immunohistochemistry staining was present in 29% of primary UCs and 49% of metastases and did not impact overall survival (P = 0.89, primary tumors; P = 0.78, metastases). FGFR3 mutations were observed in 2% of primary tumors and 9% of metastases. Mutant tumors expressed higher levels of FGFR3 mRNA than wild-type tumors (P < 0.001). FGFR3 copy number gain and loss were rare events in primary and metastatic tumors (0.8% each; 3.0% and 12.3%, respectively). FGFR3 immunohistochemistry staining is present in one third of primary muscle-invasive UCs and half of metastases, while FGFR3 mutations and copy number changes are relatively uncommon

Measuring adherence to antiretroviral treatment in resource-poor settings: The clinical validity of key indicators

<p>Abstract</p> <p>Background</p> <p>Access to antiretroviral therapy has dramatically expanded in Africa in recent years, but there are no validated approaches to measure treatment adherence in these settings.</p> <p>Methods</p> <p>In 16 health facilities, we observed a retrospective cohort of patients initiating antiretroviral therapy. We constructed eight indicators of adherence and visit attendance during the first 18 months of treatment from data in clinic and pharmacy records and attendance logs. We measured the correlation among these measures and assessed how well each predicted changes in weight and CD4 count.</p> <p>Results</p> <p>We followed 488 patients; 63.5% had 100% coverage of medicines during follow-up; 2.7% experienced a 30-day gap in treatment; 72.6% self-reported perfect adherence in all clinic visits; and 19.9% missed multiple clinic visits. After six months of treatment, mean weight gain was 3.9 kg and mean increase in CD4 count was 138.1 cells/mm3.</p> <p>Dispensing-based adherence, self-reported adherence, and consistent visit attendance were highly correlated. The first two types of adherence measure predicted gains in weight and CD4 count; consistent visit attendance was associated only with weight gain.</p> <p>Conclusions</p> <p>This study demonstrates that routine data in African health facilities can be used to monitor antiretroviral adherence at the patient and system level.</p